The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics)

Science & Math

Singer, Ivan

Mathematics

Springer

This book examines abstract convex analysis and presents the results of recent research, specifically on parametrizations of Minkowski type dualities and of conjugations of type Lau. It explains the main concepts through cases and detailed proofs.

Abstract Convex Analysis (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts)

Wiley-Interscience

Results and problems in the modern theory of best approximation, in which the methods of functional analysis are applied in a consequent manner. This modern theory constitutes both a unified foundation for the classical theory of best approximation and a powerful tool for obtaining new results.

The Theory of Best Approximation and Functional Analysis (Regional Conference Series in Applied Mathematics - Vol 13)

Computers & Technology

Programming

Society for Industrial and Applied Mathematics

The theory of convex optimization has been constantly developing over the past 30 years.  Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems.  This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity.  This manuscript will be of great interest for experts in this and related fields.

Since the appearance, in 1970, of Vol. I of the present monograph 1370], the theory of bases in Banach spaces has developed substantially. Therefore, the present volume contains only Ch. III of the monograph, instead of Ch. Ill, IV and V, as was planned initially (cp. the table of contents of Vol. I). Since this volume is a continuation of Vol. I of the same monograph, we shall refer to the results of Vol. I directly as results of Ch. I or Ch. II (without specifying Vol. I). On the other hand, sometimes we shall also mention that certain results will be considered in Vol. III (Ch. IV, V). In spite of the many new advances made in this field, the statement in the Preface to Vol. I, that "the existing books on functional analysis contain only a few results on bases", remains still valid, with the exception of the recent book [248 a] of J. Lindenstrauss and L. Tzafriri. Since we have learned about [248 a] only in 1978, in this volume there are only references to previous works, instead of [248 a]; however, this will cause no inconvenience, since the intersec tion of the present volume with [248 a] is very small. Let us also mention the appearance, since 1970, of some survey papers on bases in Banach spaces (V. D. Milman [287], [288], C. W. McArthur [275]; M. I. Kadec [204], § 3 and others).

Bases in Banach Spaces II

Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces (Grundlehren der mathematischen Wissenschaften)

See the best price to sell, buy, or rent books by Singer, Ivan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Singer, Ivan

See the best price to sell, buy, or rent books by Singer, Ivan. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics)

Abstract Convex Analysis (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts)

The Theory of Best Approximation and Functional Analysis (Regional Conference Series in Applied Mathematics - Vol 13)

Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics)

Bases in Banach Spaces II

Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces (Grundlehren der mathematischen Wissenschaften)