Foundations of Mathematical Optimization
Subtitle: Convex Analysis without Linearity
By: by Diethard Pallaschke, Stefan Rolewicz
Contributors: Rolewicz, Stefan
Series: Mathematics and Its Applications -- 388; Mathematics and Its Applications -- 388
Publisher: Springer Netherlands
Published: 1997
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 585
ISBN-13: 9789048148004; 9789401715881
Subjects: Mathematics; Mathematical optimization
Description: Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.
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