Optimization on Metric and Normed Spaces

Covering recent work on Banach and complete metric spaces, this book uses the Baire approach and considers approximate solutions. It presents new results including penalty methods in constrained optimization and extant solutions in parametric optimization.

"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.

Establishes the existence of solutions of parametric optimization problems on metric spaces. Provides solutions to well-posedness of constrained minimization problems on Banach spaces. Contains solutions to a number of difficult and common problems in optimization. Presents new approches for optimization on metric normed spaces.

Inhalt
Exact Penalty in Constrained Optimization.- Stability of the Exact Penalty.- Generic Well-Posedness of Minimization Problems.- Well-Posedness and Porosity.- Parametric Optimization.- Optimization with Increasing Objective Functions.- Generic Well-Posedness of Minimization Problems with Constraints.- Vector Optimization.- Infinite Horizon Problems.