Nonlinear Analysis : Approximation Theory, Optimization and Applications / Ed. - Ansari, Qamrul Hasan Ed. (New Delhi : Birkhauser, 2014)
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.
Chapter 1. Best Proximity Points -- Chapter 2. Semi-Continuity Properties of Metric Projections -- Chapter 3. Convergence of Slices, Geometric Aspects in Banach Spaces and Proximinality -- Chapter 4. Measures of Non compactness and Well-Posed Minimization Problems -- Chapter 5. Well-Posedness, Regularization and Viscosity Solutions of Minimization Problems -- Chapter 6. Best Approximation in Nonlinear Functional Analysis -- Chapter 7. Hierarchical Minimization Problems and Applications -- Chapter 8. Triple Hierarchical Variational Inequalities -- Chapter 9. Split Feasibility and Fixed Point Problems -- Chapter 10. Isotone Projection Cones and Nonlinear Complementarity Problems.
Keywords: Analysis (Mathematics); Approximation Theory; Calculus of Variations; Functional Analysis; Mathematical Analysis; Mathematical Optimization; Operator Theory; Analysis; Approximations and Expansions; Calculus of Variations and Optimal Control; Optimization