Optimization on Metric and Normed Spaces

Preface. - Introduction. -1. Exact penalty in constrained optimization. - 1.1. A sufficient condition for exact penalty in constrained optimization. - 1.2. Existence of exact penalty for inequality-constrained problems. - 1.3. Existence of exact penalty for optimization problems with mixed constraints in Banach spaces. - 1.4. Existence of exact penalty for constrained optimization problems in Hilbert spaces with smooth constraint and objective functions. - 1.5. Existence of exact penalty for constrained optimization problems in metric spaces. - 2. Variational principles and generic well-posedness of optimization problems. - 2.1 Generic vriational principles. - 2.2. Porosity and well-posedness of optimization problems. - 2.3. Existence of solutions for a class of minimization problems with a generic objective function. - 2.4. A generic existence result for a class of optimization problems. - 2.5. Well-posedness and porosity in convex optimization. - 2.6. A porosity result in convex optimization in reflexive Banach spaces. - 3. Parametric optimization. - 3.1. Generic existence in parametric optimization. - 3.2. Variational principles and their concretizations. - 3.3. Two generic existence results. - 3.4. A generic existence result for the problem (P). - 3.5. Existence of solutions in parametric optimization and porosity. - 3.6. Variational principles and porosity. - 3.7. Concretization of variational principles. - 3.8. Existence result for the problem (P2). - 3.9. Existence result for the problem (P1). - 3.10. Generic well-posedness in parametric optimization with constraints. - 4. Optimization with increasing objective functions. - 4.1. Generic existence of solutions of minimization problems with increasing objective functions. - 4.2. A variational principle. - 4.3. Spaces of increasing coercive functions. - 4.4. The proof of the first generic existence theorem. - 4.5. Spaces of increasing noncoercive functions. - 4.6. The proof of the second generic existence theorem. - 4.7. Spaces of increasing quasiconvex functions. - 4.8. The proof of the third generic existence result. - 4.9. Spaces of increasing convex functions. - 4.10. The proof of the fourth generic existence result. - 4.11. The generic existence result for the minimization problem (P2). - 4.12. The proof of the generic existence result for the problem (P1). - 4.13. Existence of solutions of minimization problems with an increasing objective functions and porosity. - 4.14. Well-posedness of minimization problems with increasing objective functions. - 4.15. Porosity and variational principles. - 4.16. Porosity results. - 5. Generic well-posedness of minimization problems with constraints. - 5.1. Preliminaries. - 5.2. Problems with continuous objective and constraint functions. - 5.3. Problems with smooth objective and constraint functions. - 5.4. Extensions. - 6. Vector optimization. - 6.1. Preliminaries. - 6.2. A density result. - 6.3. A generic result. - 6.4. A well-posedness result. - 7. Minimal solutions for infinite horizon problems in metric spaces. - 7.1. Preliminaries and main result. - 7.2. Auxiliary results. - 7.3. Proof of the main result. - 7.4. Properties of good sequences. - 7.5. Infinite horizon convex optimization problems in a Banach space. - References. - Index.