Foundations of Mathematical Optimization, Softcover reprint of hardcover 1st ed. 1997
Convex Analysis without Linearity
Mathematics and Its Applications Series, Vol. 388

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.

1. General Optimality.- 2. Optimization in Metric Spaces.- 3. Multifunctions and Marginal Functions in Metric Spaces.- 4. Well-Posedness and Weak Well-Posedness in Banach Spaces.- 5. Duality in Banach and Hilbert Spaces. Regularization.- 6.Necessary Conditions for Optimality and Local Optimality in Normed Spaces.- 7.Polynomials. Necessary and Sufficient Conditions of Optimality of Higher Order.- 8. Nondifferentiable Optimization.- 9. Numerical Aspects.- 10. Vector Optimization.- Author index.- List of symbols.

This volume is unique in its emphasis : the first three chapters develop optimization in spaces without linear structures, and the analog of convex analysis is constructed for this case. 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.