Optimization on Metric and Normed Spaces [electronic resource] /
Zaslavski, Alexander J.author.
"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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
"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.
Mathematical models.
Numerical analysis.
Functional analysis.
Operations research.
Management science.
Calculus of variations.
Mathematical Modeling and Industrial Mathematics.
Numerical Analysis.
Functional Analysis.
Operations Research, Management Science.
Calculus of Variations and Optimal Control; Optimization.
Springer optimization and its applications