Nonlinear Analysis: Approximation Theory, Optimization and Applications

Description

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering Front Matter....Pages i-xv Best Proximity Points....Pages 1-32 Semi-continuity Properties of Metric Projections....Pages 33-59 Convergence of Slices, Geometric Aspects in Banach Spaces and Proximinality....Pages 61-107 Measures of Noncompactness and Well-Posed Minimization Problems....Pages 109-134 Well-Posedness, Regularization, and Viscosity Solutions of Minimization Problems....Pages 135-164 Best Approximation in Nonlinear Functional Analysis....Pages 165-198 Hierarchical Minimization Problems and Applications....Pages 199-229 Triple Hierarchical Variational Inequalities....Pages 231-280 Split Feasibility and Fixed Point Problems....Pages 281-322 Isotone Projection Cones and Nonlinear Complementarity Problems....Pages 323-347 Back Matter....Pages 349-352