Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology

Description

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology. Front Matter ....Pages i-xxiv Introduction (Neculai Andrei)....Pages 1-17 Mathematical Modeling Using Algebraic Oriented Languages for Nonlinear Optimization (Neculai Andrei)....Pages 19-27 Introduction to GAMS Technology (Neculai Andrei)....Pages 29-45 Applications of Continuous Nonlinear Optimization (Neculai Andrei)....Pages 47-117 Optimality Conditions for Continuous Nonlinear Optimization (Neculai Andrei)....Pages 119-145 Simple Bound Constraints Optimization (Neculai Andrei)....Pages 147-184 Penalty and Augmented Lagrangian Methods (Neculai Andrei)....Pages 185-201 A Penalty-Barrier Algorithm: SPENBAR (Neculai Andrei)....Pages 203-221 Linearly Constrained Augmented Lagrangian: MINOS (Neculai Andrei)....Pages 223-241 Quadratic Programming (Neculai Andrei)....Pages 243-268 Sequential Quadratic Programming (SQP) (Neculai Andrei)....Pages 269-288 A SQP Method Using Only Equality-Constrained Sub-problems: DONLP (Neculai Andrei)....Pages 289-296 A SQP Algorithm with Successive Error Restoration: NLPQLP (Neculai Andrei)....Pages 297-303 Active-set Sequential Linear-Quadratic Programming: KNITRO/ACTIVE (Neculai Andrei)....Pages 305-315 A SQP Algorithm for Large-Scale Constrained Optimization: SNOPT (Neculai Andrei)....Pages 317-330 Generalized Reduced Gradient with Sequential Linearization: CONOPT (Neculai Andrei)....Pages 331-342 Interior Point Methods (Neculai Andrei)....Pages 343-380 Filter Methods (Neculai Andrei)....Pages 381-396 Interior Point Sequential Linear-Quadratic Programming: KNITRO/INTERIOR (Neculai Andrei)....Pages 397-413 Interior Point Filter Line Search: IPOPT (Neculai Andrei)....Pages 415-435 Numerical Studies: Comparisons (Neculai Andrei)....Pages 437-447 Back Matter ....Pages 449-506