Ebook: Foundations of Mathematical Optimization: Convex Analysis without Linearity

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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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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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.
Content:
Front Matter....Pages i-xii
General Optimality....Pages 1-55
Optimization in Metric Spaces....Pages 56-170
Multifunctions and marginal functions in metric spaces....Pages 171-230
Well-posedness and weak well-posedness in Banach spaces....Pages 231-293
Duality in Banach and Hilbert spaces. Regularization....Pages 294-312
Necessary conditions for optimality and local optimality in normed spaces....Pages 313-389
Polynomials. Necessary and sufficient conditions of optimality of higher order....Pages 390-411
Nondifferentiable optimization....Pages 412-468
Numerical aspects....Pages 469-496
Vector optimization....Pages 497-550
Back Matter....Pages 551-585

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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.
Content:
Front Matter....Pages i-xii
General Optimality....Pages 1-55
Optimization in Metric Spaces....Pages 56-170
Multifunctions and marginal functions in metric spaces....Pages 171-230
Well-posedness and weak well-posedness in Banach spaces....Pages 231-293
Duality in Banach and Hilbert spaces. Regularization....Pages 294-312
Necessary conditions for optimality and local optimality in normed spaces....Pages 313-389
Polynomials. Necessary and sufficient conditions of optimality of higher order....Pages 390-411
Nondifferentiable optimization....Pages 412-468
Numerical aspects....Pages 469-496
Vector optimization....Pages 497-550
Back Matter....Pages 551-585
....