Reference Encyclopedia of Optimization

Description

Z......Page 0 ABS Algorithms for Linear Equations and Linear Least Squares......Page 1 ABS Algorithms for Optimization......Page 7 Adaptive Convexification in Semi-Infinite Optimization......Page 14 Adaptive Global Search......Page 19 Adaptive Simulated Annealing and its Application to Protein Folding......Page 21 Airline Optimization......Page 26 Algorithmic Improvements Using a Heuristic Parameter, Reject Index for Interval Optimization......Page 30 Algorithms for Genomic Analysis......Page 33 Alignment Problem......Page 54 αBB Algorithm......Page 61 Alternative Set Theory......Page 73 Approximation of Extremum Problems with Probability Functionals......Page 78 Approximation ofMultivariate Probability Integrals......Page 83 Approximations to Robust Conic Optimization Problems......Page 90 Archimedes and the Foundations of Industrial Engineering......Page 96 Asset Liability Management Decision Support System......Page 98 Assignment andMatching......Page 106 Assignment Methods in Clustering......Page 108 Asymptotic Properties of Random Multidimensional Assignment Problem......Page 114 Asynchronous Distributed Optimization Algorithms......Page 123 Auction Algorithms......Page 128 Automatic Differentiation: Calculation of the Hessian......Page 133 Automatic Differentiation: Calculation of Newton Steps......Page 137 Automatic Differentiation: Geometry of Satellites and Tracking Stations......Page 142 Automatic Differentiation: Introduction, History and Rounding Error Estimation......Page 153 Automatic Differentiation: Parallel Computation......Page 159 Automatic Differentiation: Point and Interval......Page 165 Automatic Differentiation: Point and Interval Taylor Operators......Page 171 Automatic Differentiation: Root Problemand Branch Problem......Page 176 Bayesian Global Optimization......Page 182 Bayesian Networks......Page 186 Beam Selection in Radiotherapy Treatment Design......Page 195 Best Approximation in Ordered Normed Linear Spaces......Page 201 Bilevel Fractional Programming......Page 218 Bilevel Linear Programming......Page 220 Bilevel Linear Programming: Complexity, Equivalence to Minmax, Concave Programs......Page 224 Bilevel Optimization: Feasibility Test and Flexibility Index......Page 227 Bilevel Programming......Page 238 Bilevel Programming: Applications......Page 240 Bilevel Programming: Applications in Engineering......Page 242 Bilevel Programming Framework for Enterprise-Wide Process Networks Under Uncertainty......Page 247 Bilevel Programming: Global Optimization......Page 254 Bilevel Programming: Implicit Function Approach......Page 259 Bilevel Programming: Introduction, History and Overview......Page 265 Bilevel Programming in Management......Page 268 Bilevel Programming: Optimality Conditions and Duality......Page 273 Bilinear Programming......Page 278 Bilinear Programming: Applications in the Supply Chain Management......Page 281 Bi-Objective Assignment Problem......Page 287 Biquadratic Assignment Problem......Page 292 Bisection Global Optimization Methods......Page 293 Boolean and Fuzzy Relations......Page 296 Bottleneck Steiner Tree Problems......Page 310 Boundary Condition Iteration BCI......Page 312 Bounding Derivative Ranges......Page 317 Bounds and Solution Vector Estimates for Parametric NLPS......Page 324 Branch and Price: Integer Programming with Column Generation......Page 327 Branchwidth and Branch Decompositions1......Page 331 Broadcast Scheduling Problem......Page 338 Broyden Family ofMethods and the BFGS Update......Page 344 CapacitatedMinimum Spanning Trees......Page 346 Carathéodory, Constantine......Page 356 Carathéodory Theorem......Page 357 Checklist Paradigm Semantics for Fuzzy Logics......Page 358 Chemical Process Planning......Page 368 Cholesky Factorization......Page 373 CombinatorialMatrix Analysis......Page 376 Combinatorial Optimization Algorithms in Resource Allocation Problems......Page 381 Combinatorial Optimization Games......Page 386 Combinatorial Test Problems and Problem Generators......Page 390 Communication Network Assignment Problem......Page 393 Competitive Facility Location......Page 395 Competitive Ratio for Portfolio Management......Page 400 Complementarity Algorithms in Pattern Recognition......Page 404 Complexity Classes in Optimization......Page 412 Complexity of Degeneracy......Page 418 Complexity of Gradients, Jacobians, and Hessians......Page 424 Complexity and Large-Scale Least Squares Problems......Page 434 Complexity Theory......Page 446 Complexity Theory: Quadratic Programming......Page 450 Composite Nonsmooth Optimization......Page 453 Computational Complexity Theory......Page 456 Concave Programming......Page 461 Conjugate-Gradient Methods......Page 465 ContactMap OverlapMaximization Problem, CMO......Page 470 Continuous Approximations to Subdifferentials......Page 474 Continuous Global Optimization: Applications......Page 481 Continuous Global Optimization: Models, Algorithms and Software......Page 485 Continuous Reformulations of Discrete-Continuous Optimization Problems......Page 492 Continuous Review Inventory Models: (Q, R) Policy......Page 500 Contraction-Mapping......Page 504 Control Vector Iteration CVI......Page 508 Convex Discrete Optimization......Page 512 Convex Envelopes in Optimization Problems......Page 549 Convexifiable Functions, Characterization of1......Page 550 Convex Max-Functions......Page 554 Convex-Simplex Algorithm......Page 557 Copositive Optimization......Page 560 Copositive Programming......Page 563 Cost Approximation Algorithms......Page 566 Credit Rating and OptimizationMethods......Page 577 Criss-Cross Pivoting Rules......Page 583 Cutting PlaneMethods for Global Optimization......Page 589 Cutting-Stock Problem......Page 593 Cyclic Coordinate Method......Page 594 Data Envelopment Analysis......Page 596 Data Mining......Page 599 D.C. Programming......Page 606 Decision Support Systems withMultiple Criteria......Page 611 Decomposition Algorithms for the Solution of Multistage Mean-Variance Optimization Problems......Page 618 Decomposition in Global Optimization......Page 626 Decomposition Principle of Linear Programming......Page 629 Decomposition Techniques forMILP: Lagrangian Relaxation......Page 631 De Novo Protein Design Using Flexible Templates......Page 637 De Novo Protein Design Using Rigid Templates......Page 642 Derivative-FreeMethods for Non-smooth Optimization......Page 647 Derivatives ofMarkov Processes and Their Simulation......Page 654 Derivatives of Probability and Integral Functions: General Theory and Examples......Page 657 Derivatives of Probability Measures......Page 663 Design Optimization in Computational Fluid Dynamics......Page 665 Design of Robust Model-Based Controllers via Parametric Programming......Page 676 Determining the Optimal Number of Clusters......Page 686 Deterministic and Probabilistic OptimizationModels for Data Classification......Page 693 Differential Equations and Global Optimization......Page 701 Dini and Hadamard Derivatives in Optimization......Page 709 Directed Tree Networks......Page 715 Direct Global Optimization Algorithm......Page 724 Direct Search Luus–Jaakola Optimization Procedure......Page 734 Discontinuous Optimization......Page 738 Discretely Distributed Stochastic Programs: Descent Directions and Efficient Points......Page 743 Discrete Stochastic Optimization......Page 750 Disease Diagnosis: Optimization-BasedMethods......Page 752 Disjunctive Programming......Page 783 Distance Dependent Protein Force Field via Linear Optimization......Page 786 Domination Analysis in Combinatorial Optimization......Page 791 Duality Gaps in Nonconvex Optimization......Page 801 Duality in Optimal Control with First Order Differential Equations......Page 804 Duality for Semidefinite Programming......Page 810 Duality Theory: Biduality in Nonconvex Optimization......Page 813 Duality Theory: Monoduality in Convex Optimization......Page 817 Duality Theory: Triduality in Global Optimization......Page 821 Dykstra’s Algorithm and Robust Stopping Criteria......Page 827 Dynamic Programming: Average Cost Per Stage Problems......Page 832 Dynamic Programming in Clustering......Page 836 Dynamic Programming: Continuous-time Optimal Control......Page 843 Dynamic Programming: Discounted Problems......Page 845 Dynamic Programming: Infinite Horizon Problems, Overview......Page 849 Dynamic Programming: Inventory Control......Page 852 Dynamic Programming and Newton’sMethod in Unconstrained Optimal Control......Page 855 Dynamic Programming: Optimal Control Applications......Page 861 Dynamic Programming: Stochastic Shortest Path Problems......Page 868 Dynamic Programming: Undiscounted Problems......Page 872 Dynamic Traffic Networks......Page 875 Economic Lot-Sizing Problem......Page 882 Eigenvalue Enclosures for Ordinary Differential Equations......Page 886 EllipsoidMethod......Page 889 Emergency Evacuation, OptimizationModeling......Page 899 Entropy Optimization: Interior PointMethods......Page 906 Entropy Optimization: Parameter Estimation......Page 911 Entropy Optimization: ShannonMeasure of Entropy and its Properties......Page 915 Equality-Constrained Nonlinear Programming: KKT Necessary Optimality Conditions......Page 920 Equilibrium Networks......Page 922 Equivalence Between Nonlinear Complementarity Problem and Fixed Point Problem......Page 926 Estimating Data forMulticriteria Decision Making Problems: Optimization Techniques......Page 930 Evacuation Networks......Page 939 Evolutionary Algorithms in Combinatorial Optimization......Page 949 Extended Cutting Plane Algorithm......Page 958 Extension of the Fundamental Theorem of Linear Programming......Page 965 Extremum Problems with Probability Functions: Kernel Type Solution Methods......Page 968 Facilities Layout Problems......Page 973 Facility Location with Externalities......Page 977 Facility Location Problems with Spatial Interaction......Page 980 Facility Location with Staircase Costs......Page 987 Farkas Lemma......Page 993 Farkas Lemma: Generalizations......Page 996 Feasible Sequential Quadratic Programming......Page 999 Feedback Set Problems......Page 1003 FejérMonotonicity in Convex Optimization......Page 1014 Financial Applications of Multicriteria Analysis......Page 1022 Financial Equilibrium......Page 1033 Financial Optimization......Page 1038 Finite Complete Systems of Many-valued Logic Algebras......Page 1046 First Order Constraint Qualifications......Page 1053 Flow Shop Scheduling Problem......Page 1058 Forecasting......Page 1066 Fourier–Motzkin EliminationMethod......Page 1072 Fractional Combinatorial Optimization......Page 1075 Fractional Programming......Page 1078 Fractional Zero-One Programming......Page 1089 Frank–Wolfe Algorithm......Page 1092 Frequency Assignment Problem......Page 1095 Fundamental Theorem of Algebra......Page 1099 FuzzyMulti-objective Linear Programming......Page 1101 Gasoline Blending and Distribution Scheduling: AnMILPModel......Page 1111 Gauss, Carl Friedrich......Page 1125 Gauss–NewtonMethod: Least Squares, Relation to Newton’s Method......Page 1127 Gene Clustering: A Novel Decomposition-Based Clustering Approach: Global Optimum Search with Enhanced Positioning......Page 1132 Generalizations of Interior Point Methods for the Linear Complementarity Problem......Page 1143 Generalized Assignment Problem......Page 1151 Generalized Benders Decomposition......Page 1160 Generalized Concavity inMulti-objective Optimization......Page 1173 Generalized Disjunctive Programming......Page 1178 Generalized Eigenvalue Proximal Support VectorMachine Problem......Page 1181 Generalized Geometric Programming: Mixed Continuous and Discrete Free Variables......Page 1183 GeneralizedMonotone MultivaluedMaps......Page 1191 GeneralizedMonotone Single ValuedMaps......Page 1195 GeneralizedMonotonicity: Applications to Variational Inequalities and Equilibrium Problems......Page 1200 Generalized Networks......Page 1207 Generalized Nonlinear Complementarity Problem......Page 1212 Generalized Outer Approximation......Page 1213 Generalized Primal-relaxed Dual Approach......Page 1221 Generalized Semi-infinite Programming: Optimality Conditions......Page 1225 Generalized Total Least Squares......Page 1231 Generalized Variational Inequalities: A Brief Review......Page 1236 GeneralMoment Optimization Problems......Page 1242 General Routing Problem......Page 1250 Genetic Algorithms......Page 1252 Genetic Algorithms for Protein Structure Prediction......Page 1255 Geometric Programming......Page 1258 Global Equilibrium Search......Page 1266 Globally Convergent HomotopyMethods......Page 1270 Global Optimization Algorithms for Financial Planning Problems......Page 1275 Global Optimization in the Analysis and Management of Environmental Systems......Page 1280 Global Optimization: Application to Phase Equilibrium Problems......Page 1284 Global Optimization Based on StatisticalModels......Page 1289 Global Optimization in Batch Design Under Uncertainty......Page 1292 Global Optimization in Binary Star Astronomy......Page 1297 Global Optimization: Cutting AngleMethod......Page 1302 Global Optimization: Envelope Representation......Page 1309 Global Optimization: Filled FunctionMethods......Page 1314 Global Optimization: Functional Forms......Page 1321 Global Optimization: g- ˛ BB Approach......Page 1326 Global Optimization in Generalized Geometric Programming......Page 1331 Global Optimization of Heat Exchanger Networks......Page 1335 Global Optimization: Hit and RunMethods......Page 1340 Global Optimization: Interval Analysis and Balanced Interval Arithmetic......Page 1344 Global Optimization in Lennard–Jones andMorse Clusters......Page 1348 Global Optimization in Location Problems......Page 1352 Global OptimizationMethods for Harmonic Retrieval......Page 1357 Global OptimizationMethods for Systems of Nonlinear Equations......Page 1362 Global Optimization inMultiplicative Programming......Page 1364 Global Optimization: p- ˛ BB Approach......Page 1368 Global Optimization in Phase and Chemical Reaction Equilibrium......Page 1374 Global Optimization of Planar Multilayered Dielectric Structures......Page 1381 Global Optimization in Protein Folding......Page 1390 Global Optimization: Tight Convex Underestimators......Page 1409 Global Optimization Using Space Filling......Page 1416 Global Optimization in Weber’s Problem with Attraction and Repulsion......Page 1421 Global Pairwise Protein Sequence Alignment viaMixed-Integer Linear Optimization......Page 1425 Global Supply ChainModels......Page 1432 Global TerrainMethods......Page 1435 Graph Coloring......Page 1442 Graph Planarization......Page 1446 Graph Realization via Semidefinite Programming......Page 1451 Greedy Randomized Adaptive Search Procedures......Page 1458 Gröbner Bases for Polynomial Equations......Page 1467 Hamilton–Jacobi–Bellman Equation......Page 1470 Hemivariational Inequalities: Applications inMechanics......Page 1474 Hemivariational Inequalities: Eigenvalue Problems......Page 1480 Hemivariational Inequalities: Static Problems......Page 1485 Heuristic andMetaheuristic Algorithms for the Traveling Salesman Problem......Page 1496 Heuristic Search......Page 1503 Heuristics forMaximum Clique and Independent Set......Page 1505 High-order Maximum Principle for Abnormal Extremals......Page 1517 High-order Necessary Conditions for Optimality for Abnormal Points......Page 1524 Hilbert’s Thirteenth Problem......Page 1532 History of Optimization......Page 1535 Homogeneous SelfdualMethods for Linear Programming......Page 1539 Hyperplane Arrangements......Page 1542 Hyperplane Arrangements in Optimization......Page 1544 IdentificationMethods for Reaction Kinetics and Transport......Page 1546 Ill-posed Variational Problems......Page 1553 Image Space Approach to Optimization......Page 1558 Implicit Lagrangian......Page 1564 Increasing and Convex-Along-Rays Functions on Topological Vector Spaces......Page 1568 Increasing and Positively Homogeneous Functions on Topological Vector Spaces......Page 1573 Inequality-constrained Nonlinear Optimization......Page 1583 Inference ofMonotone Boolean Functions......Page 1588 Infinite Horizon Control and Dynamic Games......Page 1595 Information-based Complexity and Information-based Optimization......Page 1600 Integer Linear Complementary Problem......Page 1605 Integer Linear Programs for Routing and Protection Problems in Optical Networks......Page 1607 Integer Programming......Page 1614 Integer Programming: AlgebraicMethods......Page 1621 Integer Programming: Branch and Bound Methods......Page 1631 Integer Programming: Branch and Cut Algorithms......Page 1640 Integer Programming: Cutting Plane Algorithms......Page 1647 Integer Programming Duality......Page 1654 Integer Programming: Lagrangian Relaxation......Page 1664 Integrated Planning and Scheduling......Page 1670 Interior PointMethods for Semidefinite Programming......Page 1676 Interval Analysis: Application to Chemical Engineering Design Problems......Page 1680 Interval Analysis: Differential Equations......Page 1683 Interval Analysis: Eigenvalue Bounds of IntervalMatrices......Page 1686 Interval Analysis: Intermediate Terms......Page 1693 Interval Analysis: Nondifferentiable Problems......Page 1696 Interval Analysis for Optimization of Dynamical Systems......Page 1699 Interval Analysis: ParallelMethods for Global Optimization......Page 1706 Interval Analysis: Subdivision Directions in Interval Branch and Bound Methods......Page 1714 Interval Analysis: Systems of Nonlinear Equations......Page 1718 Interval Analysis: Unconstrained and Constrained Optimization......Page 1724 Interval Analysis: Verifying Feasibility......Page 1727 Interval Constraints......Page 1730 Interval Fixed Point Theory......Page 1733 Interval Global Optimization......Page 1736 Interval Linear Systems......Page 1754 Interval NewtonMethods......Page 1760 InventoryManagement in Supply Chains......Page 1763 Invexity and its Applications......Page 1767 Isotonic Regression Problems......Page 1771 Jaynes’ Maximum Entropy Principle......Page 1775 Job-shop Scheduling Problem......Page 1778 Kantorovich, Leonid Vitalyevich......Page 1785 Kolmogorov Complexity......Page 1786 Kuhn–Tucker Optimality Conditions......Page 1790 Lagrange, Joseph-Louis......Page 1794 Lagrange-Type Functions......Page 1795 Lagrangian Duality: BASICS......Page 1800 Lagrangian MultipliersMethods for Convex Programming......Page 1808 LaplaceMethod and Applications to Optimization Problems......Page 1813 Large Scale Trust Region Problems......Page 1817 Large Scale Unconstrained Optimization......Page 1826 L-convex Functions andM-convex Functions......Page 1833 LCP: Pardalos–Rosen Mixed Integer Formulation......Page 1840 Least-index Anticycling Rules......Page 1842 Least Squares Orthogonal Polynomials......Page 1846 Least Squares Problems......Page 1851 Leibniz, Gottfried Wilhelm......Page 1861 LemkeMethod......Page 1863 Lexicographic Pivoting Rules......Page 1865 Linear Complementarity Problem......Page 1869 Linear Optimization: Theorems of the Alternative......Page 1873 Linear Ordering Problem......Page 1876 Linear Programming......Page 1878 Linear Programming: Interior PointMethods......Page 1881 Linear Programming: Karmarkar Projective Algorithm......Page 1884 Linear Programming: Klee–Minty Examples......Page 1886 Linear Programming Models for Classification......Page 1892 Linear Space......Page 1896 Lipschitzian Operators in Best Approximation by Bounded or Continuous Functions......Page 1897 Load Balancing for Parallel Optimization Techniques......Page 1900 Local Attractors for Gradient-related Descent Iterations......Page 1906 Location Routing Problem......Page 1914 Logconcave Measures, Logconvexity......Page 1920 Logconcavity of Discrete Distributions......Page 1922 Logic-Based Outer Approximation......Page 1923 Lovász Number......Page 1927 LP Strategy for Interval-Newton Method in Deterministic Global Optimization......Page 1932 L-shapedMethod for Two-stage Stochastic Programs with Recourse......Page 1938 Maritime Inventory Routing Problems......Page 1941 Mathematical Programming for DataMining......Page 1949 Mathematical Programming Methods in Supply Chain Management......Page 1953 Matrix Completion Problems......Page 1961 Matroids......Page 1969 Maximum Constraint Satisfaction: Relaxations and Upper Bounds......Page 1975 Maximum Cut Problem, MAX-CUT......Page 1985 Maximum Entropy and Game Theory......Page 1993 Maximum Entropy Principle: Image Reconstruction......Page 1998 Maximum Flow Problem......Page 2003 Maximum Likelihood Detection via Semidefinite Programming......Page 2014 Maximum PartitionMatching......Page 2023 Maximum Satisfiability Problem......Page 2029 Medium-Term Scheduling of Batch Processes......Page 2035 Metaheuristic Algorithms for the Vehicle Routing Problem......Page 2049 Metaheuristics......Page 2055 Minimax: Directional Differentiability......Page 2069 Minimax Game Tree Searching......Page 2073 Minimax Theorems......Page 2081 Minimum Concave Transportation Problems......Page 2087 Minimum Cost Flow Problem......Page 2089 MINLP: Application in Facility Location-allocation......Page 2102 MINLP: Applications in Blending and Pooling Problems......Page 2108 MINLP: Applications in the Interaction of Design and Control......Page 2115 MINLP: Branch and Bound Global Optimization Algorithm......Page 2126 MINLP: Branch and Bound Methods......Page 2132 MINLP: Design and Scheduling of Batch Processes......Page 2136 MINLP: Generalized Cross Decomposition......Page 2142 MINLP: Global Optimization with ˛ BB......Page 2149 MINLP: Heat Exchanger Network Synthesis......Page 2157 MINLP: Logic-basedMethods......Page 2164 MINLP: Mass and Heat Exchanger Networks......Page 2167 MINLP: Outer Approximation Algorithm......Page 2173 MINLP: Reactive Distillation Column Synthesis......Page 2177 MINLP: Trim-loss Problem......Page 2184 Mixed 0-1 Linear Programming Approach for DNA Transcription Element Identification......Page 2193 Mixed Integer Classification Problems......Page 2204 Mixed Integer Linear Programming: Heat Exchanger Network Synthesis......Page 2208 Mixed Integer Linear Programming: Mass and Heat Exchanger Networks......Page 2211 Mixed Integer Nonlinear Bilevel Programming: Deterministic Global Optimization......Page 2219 Mixed-Integer Nonlinear Optimization: A Disjunctive Cutting Plane Approach......Page 2224 Mixed Integer Nonlinear Programming......Page 2228 Mixed Integer Optimization in Well Scheduling......Page 2241 Mixed Integer Programming/Constraint Programming Hybrid Methods......Page 2264 Model Based Control for Drug Delivery Systems......Page 2270 Modeling Difficult Optimization Problems......Page 2278 Modeling Languages in Optimization: A New Paradigm......Page 2291 Molecular Distance Geometry Problem......Page 2299 Molecular Structure Determination: Convex Global Underestimation......Page 2305 Monotonic Optimization......Page 2310 Monte-Carlo Simulated Annealing in Protein Folding......Page 2317 Monte-Carlo Simulations for Stochastic Optimization......Page 2331 Motzkin Transposition Theorem......Page 2339 Multi-Class Data Classification viaMixed-Integer Optimization......Page 2342 Multicommodity Flow Problems......Page 2348 Multicriteria Decision Support Methodologies for Auditing Decisions......Page 2356 MulticriteriaMethods forMergers and Acquisitions......Page 2366 Multicriteria SortingMethods......Page 2373 Multidimensional Assignment Problem......Page 2390 Multidimensional Knapsack Problems......Page 2396 MultidisciplinaryDesign Optimization......Page 2400 Multifacility and Restricted Location Problems......Page 2403 Multi-index Transportation Problems......Page 2407 Multilevel Methods for Optimal Design......Page 2413 Multilevel Optimization in Mechanics......Page 2422 Multi-objective Combinatorial Optimization......Page 2431 Multi-objective Fractional Programming Problems......Page 2436 Multi-objective Integer Linear Programming......Page 2442 Multi-objectiveMixed Integer Programming......Page 2448 Multi-objective Optimization and Decision Support Systems......Page 2454 Multi-objective Optimization: Interaction of Design and Control......Page 2459 Multi-objectiveOptimization: InteractiveMethods for Preference Value Functions......Page 2465 Multi-objective Optimization: Lagrange Duality......Page 2468 Multi-objective Optimization: Pareto Optimal Solutions, Properties......Page 2472 Multiparametric Linear Programming......Page 2476 MultiparametricMixed Integer Linear Programming......Page 2478 MultipleMinima Problem in Protein Folding: ˛ BB Global Optimization Approach......Page 2484 Multiple Objective Dynamic Programming......Page 2491 Multiple Objective Programming Support......Page 2497 Multiplicative Programming......Page 2505 Multi-Quadratic Integer Programming: Models and Applications......Page 2507 Multi-Scale Global Optimization Using Terrain/Funneling Methods......Page 2514 Multistage Stochastic Programming: Barycentric Approximation......Page 2521 Nested Partitions Optimization......Page 2526 Network Design Problems......Page 2532 Network Location: Covering Problems......Page 2538 Neural Networks for Combinatorial Optimization......Page 2540 Neuro-Dynamic Programming......Page 2548 New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization......Page 2553 Nonconvex Energy Functions: Hemivariational Inequalities......Page 2564 Nonconvex Network Flow Problems......Page 2571 Nonconvex-nonsmooth Calculus of Variations......Page 2574 Nondifferentiable Optimization......Page 2577 Nondifferentiable Optimization: Cutting PlaneMethods......Page 2583 Nondifferentiable Optimization: Minimax Problems......Page 2588 Nondifferentiable Optimization: Newton Method......Page 2595 Nondifferentiable Optimization: Parametric Programming......Page 2600 Nondifferentiable Optimization: RelaxationMethods......Page 2608 Nondifferentiable Optimization: Subgradient OptimizationMethods......Page 2611 Nonlinear Least Squares: Newton-typeMethods......Page 2612 Nonlinear Least Squares Problems......Page 2619 Nonlinear Least Squares: Trust RegionMethods......Page 2623 Nonlinear Systems of Equations: Application to the Enclosure of All Azeotropes......Page 2630 Nonlocal Sensitivity Analysis with Automatic Differentiation......Page 2635 NonorientedMulticommodity Flow Problems......Page 2640 Nonsmooth Analysis: Fréchet Subdifferentials......Page 2644 Nonsmooth Analysis: Weak Stationarity......Page 2651 Nonsmooth Optimization Approach to Clustering......Page 2658 Nonsmooth and Smoothing Methods for Nonlinear Complementarity Problems and Variational Inequalities......Page 2664 NP-complete Problems and Proof Methodology......Page 2668 NumericalMethods for Unary Optimization......Page 2675 OligopolisticMarket Equilibrium......Page 2683 Operations Research......Page 2686 Operations Research and Financial Markets......Page 2688 Operations Research Models for Supply Chain Management and Design......Page 2696 Optimal Control of a Flexible Arm......Page 2707 Optimal Design of Composite Structures......Page 2710 Optimal Design in Nonlinear Optics......Page 2717 Optimality Criteria forMultiphase Chemical Equilibrium......Page 2723 Optimal Planning of Offshore Oilfield Infrastructure......Page 2730 Optimal Sensor Scheduling......Page 2738 Optimal Solvent Design Approaches......Page 2742 Optimal Triangulations......Page 2749 Optimization in Ad Hoc Networks......Page 2756 Optimization Based Framework for Radiation Therapy......Page 2766 Optimization-Based Visualization......Page 2777 Optimization in Boolean Classification Problems......Page 2783 Optimization in Classifying Text Documents......Page 2788 Optimization and Decision Support Systems......Page 2795 Optimization with Equilibrium Constraints: A Piecewise SQP Approach......Page 2799 Optimization in Leveled Graphs......Page 2805 Optimization inMedical Imaging......Page 2812 Optimization in Operation of Electric and Energy Power Systems......Page 2816 Optimization Problems in Unit-Disk Graphs......Page 2824 Optimization Software......Page 2836 Optimization Strategies for Dynamic Systems......Page 2839 Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data......Page 2850 Optimization in Water Resources......Page 2855 Optimizing Facility Location with Euclidean and Rectilinear Distances......Page 2861 Order Complementarity......Page 2865 Oriented Matroids......Page 2870 Orthogonal Triangularization......Page 2878 OutrankingMethods......Page 2879 Overdetermined Systems of Linear Equations......Page 2886 Packet Annealing......Page 2889 Parallel Computing: Complexity Classes......Page 2892 Parallel Computing: Models......Page 2895 Parallel Heuristic Search......Page 2900 Parametric Global Optimization: Sensitivity......Page 2904 Parametric Linear Programming: Cost Simplex Algorithm......Page 2909 Parametric Mixed Integer Nonlinear Optimization......Page 2912 Parametric Optimization: Embeddings, Path Following and Singularities......Page 2916 Peptide Identification viaMixed-Integer Optimization......Page 2922 Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization......Page 2930 Phase Problem in X-ray Crystallography: Shake and Bake Approach......Page 2945 Piecewise Linear Network Flow Problems......Page 2950 Pivoting Algorithms for Linear Programming Generating Two Paths......Page 2957 Planning in the Process Industry......Page 2962 Plant Layout Problems and Optimization......Page 2971 Pontryagin Maximum Principle......Page 2979 Portfolio Selection: MarkowitzMean-varianceModel......Page 2982 Portfolio Selection andMulticriteria Analysis......Page 2988 Potential ReductionMethods for Linear Programming......Page 3000 PowellMethod......Page 3004 Practical Augmented Lagrangian Methods......Page 3006 PredictiveMethod for Interhelical Contacts in Alpha-Helical Proteins......Page 3015 Preference Disaggregation......Page 3023 Preference Disaggregation Approach: Basic Features, Examples fromFinancial DecisionMaking......Page 3034 Preference Modeling......Page 3047 Preprocessing in Stochastic Programming......Page 3050 Price of Robustness for Linear Optimization Problems......Page 3053 Principal PivotingMethods for Linear Complementarity Problems......Page 3059 Probabilistic Analysis of Simplex Algorithms......Page 3065 Probabilistic Constrained Linear Programming: Duality Theory......Page 3076 Probabilistic Constrained Problems: Convexity Theory......Page 3079 Production-Distribution System Design Problem......Page 3080 Protein Folding: Generalized-Ensemble Algorithms......Page 3090 Protein Loop Structure PredictionMethods......Page 3092 Pseudomonotone Maps: Properties and Applications......Page 3097 QBB Global OptimizationMethod......Page 3103 QR Factorization......Page 3108 Quadratic Assignment Problem......Page 3111 Quadratic Fractional Programming: Dinkelbach Method......Page 3141 Quadratic Integer Programming: Complexity and Equivalent Forms......Page 3145 Quadratic Knapsack......Page 3151 Quadratic Programming with Bound Constraints......Page 3153 Quadratic Programming over an Ellipsoid......Page 3158 Quadratic Semi-assignment Problem......Page 3162 QuasidifferentiableOptimization......Page 3163 QuasidifferentiableOptimization: Algorithms for Hypodifferentiable Functions......Page 3168 QuasidifferentiableOptimization: Algorithms for QD Functions......Page 3170 QuasidifferentiableOptimization: Applications......Page 3176 Quasidifferentiable Optimization: Applications to Thermoelasticity......Page 3179 QuasidifferentiableOptimization: Calculus of Quasidifferentials......Page 3182 QuasidifferentiableOptimization: Codifferentiable Functions......Page 3186 Quasidifferentiable Optimization: Dini Derivatives, Clarke Derivatives......Page 3189 QuasidifferentiableOptimization: Exact Penalty Methods......Page 3192 Quasidifferentiable Optimization: Optimality Conditions......Page 3197 Quasidifferentiable Optimization: Stability of Dynamic Systems......Page 3205 QuasidifferentiableOptimization: Variational Formulations......Page 3209 Quasivariational Inequalities......Page 3213 Railroad Crew Scheduling......Page 3219 Railroad Locomotive Scheduling......Page 3228 Random Search Methods......Page 3237 Reactive Scheduling of Batch Processes......Page 3243 Redundancy in Nonlinear Programs......Page 3254 Reformulation-Linearization Technique for Global Optimization......Page 3255 Regression by Special Functions: Algorithms and Complexity......Page 3260 Relaxation in Projection Methods......Page 3265 Replicator Dynamics in Combinatorial Optimization......Page 3271 Resource Allocation for Epidemic Control......Page 3283 Reverse Convex Optimization......Page 3287 Robust Control......Page 3292 Robust Control: Schur Stability of Polytopes of Polynomials......Page 3297 Robust Design of Dynamic Systems by Constructive Nonlinear Dynamics......Page 3299 Robust Global Optimization......Page 3306 Robust Linear Programming with Right-Hand-Side Uncertainty, Duality and Applications......Page 3309 Robust Optimization......Page 3319 Robust Optimization: Mixed-Integer Linear Programs......Page 3323 Rosenbrock Method......Page 3335 Rosen’sMethod, Global Convergence, and Powell’s Conjecture......Page 3337 Saddle Point Theory and Optimality Conditions......Page 3347 Second Order Constraint Qualifications......Page 3349 Second Order Optimality Conditions for Nonlinear Optimization......Page 3353 Selection ofMaximally Informative Genes......Page 3357 Selfdual ParametricMethod for Linear Programs......Page 3366 Semidefinite Programming and Determinant Maximization......Page 3367 Semidefinite Programming: Optimality Conditions and Stability......Page 3372 Semidefinite Programming and the Sensor Network Localization Problem, SNLP......Page 3377 Semidefinite Programming and Structural Optimization......Page 3382 Semi-infinite Programming and Applications in Finance......Page 3388 Semi-infinite Programming: ApproximationMethods......Page 3397 Semi-infinite Programming and Control Problems......Page 3400 Semi-infinite Programming: DiscretizationMethods......Page 3409 Semi-infinite Programming: Methods for Linear Problems......Page 3416 Semi-infinite Programming: NumericalMethods......Page 3421 Semi-infinite Programming: Second Order Optimality Conditions......Page 3426 Semi-infinite Programming, Semidefinite Programming and Perfect Duality......Page 3431 Sensitivity Analysis of Complementarity Problems......Page 3437 Sensitivity Analysis of Variational Inequality Problems......Page 3439 Sensitivity and Stability in NLP......Page 3442 Sensitivity and Stability in NLP: Approximation......Page 3446 Sensitivity and Stability in NLP: Continuity and Differential Stability......Page 3459 Sequential Cutting Plane Algorithm......Page 3463 Sequential Quadratic Programming: Interior PointMethods for DistributedOptimal Control Problems......Page 3468 Sequential SimplexMethod......Page 3471 Set Covering, Packing and Partitioning Problems......Page 3474 Set-valued Optimization......Page 3478 Shape Optimization......Page 3480 Shape ReconstructionMethods for Nonconvex Feasibility Analysis......Page 3483 Shape Selective Zeolite Separation and Catalysis: OptimizationMethods......Page 3492 Shor, Naum Zuselevich......Page 3497 Shortest Path Tree Algorithms......Page 3499 Short-Term Scheduling of Batch Processes with Resources......Page 3511 Short-Term Scheduling of Continuous Processes......Page 3525 Short-Term Scheduling, Resource Constrained: UnifiedModeling Frameworks......Page 3539 Short-Term Scheduling Under Uncertainty: Sensitivity Analysis......Page 3552 Signal Processing with Higher Order Statistics......Page 3559 Simple Recourse Problem: Dual Method......Page 3563 Simple Recourse Problem: PrimalMethod......Page 3565 Simplicial Decomposition......Page 3567 Simplicial Decomposition Algorithms......Page 3571 Simplicial Pivoting Algorithms for Integer Programming......Page 3577 Simulated Annealing......Page 3583 Simulated AnnealingMethods in Protein Folding......Page 3585 Simultaneous Estimation and Optimization of Nonlinear Problems......Page 3590 Single Facility Location: Circle Covering Problem......Page 3599 Single Facility Location: Multi-objective Euclidean Distance Location......Page 3602 Single Facility Location: Multi-objective Rectilinear Distance Location......Page 3605 Smoothing Methods for Semi-Infinite Optimization......Page 3609 Smooth Nonlinear Nonconvex Optimization......Page 3614 Solution Methods for Multivalued Variational Inequalities......Page 3617 Solving Hemivariational Inequalities by Nonsmooth Optimization Methods......Page 3631 Solving Large Scale and Sparse Semidefinite Programs......Page 3635 Spatial Price Equilibrium......Page 3639 Spectral Projected GradientMethods......Page 3644 SplittingMethod for Linear Complementarity Problems......Page 3651 SSCMinimization Algorithms......Page 3654 SSCMinimization Algorithms for Nonsmooth and Stochastic Optimization......Page 3657 Stabilization of Cutting Plane Algorithms for Stochastic Linear Programming Problems......Page 3661 Stable Set Problem: Branch & Cut Algorithms......Page 3668 Standard Quadratic Optimization Problems: Algorithms......Page 3680 Standard Quadratic Optimization Problems: Applications......Page 3682 Standard Quadratic Optimization Problems: Theory......Page 3684 State of the Art inModeling Agricultural Systems......Page 3686 Static Resource Constrained Project Scheduling......Page 3696 Static Stochastic Programming Models......Page 3700 Static Stochastic Programming Models: Conditional Expectations......Page 3702 Statistical Classification: Optimization Approaches......Page 3703 Statistical Convergence and Turnpike Theory......Page 3705 Steiner Ratio of Biomolecular Structures......Page 3710 Steiner Tree Problems......Page 3715 Stochastic Bilevel Programs......Page 3728 Stochastic Global Optimization: Stopping Rules......Page 3735 Stochastic Global Optimization: Two-PhaseMethods......Page 3738 Stochastic Integer Programming: Continuity, Stability, Rates of Convergence......Page 3742 Stochastic Integer Programs......Page 3745 Stochastic Linear Programming: Decomposition and Cutting Planes......Page 3747 Stochastic Linear Programs with Recourse and Arbitrary Multivariate Distributions......Page 3752 Stochastic Network Problems: Massively Parallel Solution......Page 3757 Stochastic Optimal Stopping: NumericalMethods......Page 3765 Stochastic Optimal Stopping: ProblemFormulations......Page 3767 Stochastic Programming: Minimax Approach......Page 3770 Stochastic Programming Models: Random Objective......Page 3774 Stochastic Programming: Nonanticipativity and LagrangeMultipliers......Page 3775 Stochastic Programming: Parallel Factorization of StructuredMatrices......Page 3782 Stochastic Programming with Simple Integer Recourse......Page 3787 Stochastic Programs with Recourse: Upper Bounds......Page 3789 Stochastic QuasigradientMethods......Page 3794 Stochastic QuasigradientMethods: Applications......Page 3799 Stochastic QuasigradientMethods inMinimax Problems......Page 3805 Stochastic Scheduling......Page 3810 Stochastic Transportation and Location Problems......Page 3816 Stochastic Vehicle Routing Problems......Page 3821 Structural Optimization......Page 3824 Structural Optimization: History......Page 3826 Suboptimal Control......Page 3828 Successive Quadratic Programming......Page 3831 Successive Quadratic Programming: Applications in Distillation Systems......Page 3838 Successive Quadratic Programming: Applications in the Process Industry......Page 3845 Successive Quadratic Programming: DecompositionMethods......Page 3858 Successive Quadratic Programming: Full SpaceMethods......Page 3863 Successive Quadratic Programming: Solution by Active Sets and Interior Point Methods......Page 3870 Supply Chain Performance Measurement......Page 3876 Survivable Networks......Page 3881 Symmetric Systems of Linear Equations......Page 3884 Theorems of the Alternative and Optimization......Page 3887 Time-Dependent Traveling Salesman Problem......Page 3894 Topological Derivative in Shape Optimization......Page 3900 TopologicalMethods in Complementarity Theory......Page 3910 Topology of Global Optimization......Page 3914 Topology Optimization......Page 3920 Traffic Network Equilibrium......Page 3921 Traveling Salesman Problem......Page 3927 Tucker Homogeneous Systems of Linear Relations......Page 3936 Turnpike Theory: Stability of Optimal Trajectories......Page 3940 Two-Stage Stochastic Programming: QuasigradientMethod......Page 3947 Two-Stage Stochastic Programs with Recourse......Page 3951 Unconstrained Nonlinear Optimization: Newton–Cauchy Framework......Page 3954 Unconstrained Optimization in Neural Network Training......Page 3959 Variable Neighborhood Search Methods......Page 3966 Variational Inequalities......Page 3980 Variational Inequalities: F. E. Approach......Page 3985 Variational Inequalities: Geometric Interpretation, Existence and Uniqueness......Page 3990 Variational Inequalities: Projected Dynamical System......Page 3993 Variational Principles......Page 3998 Vector Optimization......Page 4002 Vector Variational Inequalities......Page 4005 Vehicle Routing......Page 4010 Vehicle Routing Problem with Simultaneous Pickups and Deliveries......Page 4013 Vehicle Scheduling......Page 4018 Volume Computation for Polytopes: Strategies and Performances......Page 4023 Von Neumann, John......Page 4029 Voronoi Diagrams in Facility Location......Page 4031 Walrasian Price Equilibrium......Page 4037 Warehouse Location Problem......Page 4040 Wastewater System, Optimization of......Page 4045 Young Programming......Page 4051