Optimization on Metric and Normed Spaces [electronic resource] / by Alexander J. Zaslavski.

By: Zaslavski, Alexander J [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Springer Optimization and Its Applications: 44Publisher: New York, NY : Springer New York, 2010Description: XIV, 434 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387886213Subject(s): Mathematics | Functional analysis | Numerical analysis | Mathematical models | Calculus of variations | Operations research | Management science | Mathematics | Mathematical Modeling and Industrial Mathematics | Numerical Analysis | Functional Analysis | Operations Research, Management Science | Calculus of Variations and Optimal Control; OptimizationAdditional physical formats: Printed edition:: No titleDDC classification: 003.3 LOC classification: TA342-343Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: "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.
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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.

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