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Duality for Nonconvex Approximation and Optimization

Duality for Nonconvex Approximation and Optimization more books like this

by Ivan Singer

The theory of convex optimization has been developing constantly over the past 30 years. Recently, 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" optimization problems. This monograph contains an exhaustive presentation of the ...

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Convexity

Convexity more books like this

by Webster

Convexity provides a wide-ranging introduction for final year undergraduates and graduate students. Convex sets and functions are studied in the Euclidean space IRn, thus allowing an exposition demanding only an elementary knowledge of analysis and linear algebra, and enabling concepts to be motivated through simple geometric examples. The ...

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Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds

Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds more books like this

by Vitali D Milman, Gideon Schechtman

Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related ...

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Convex Sets and Their Applications

Convex Sets and Their Applications more books like this

by Steven R Lay

Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity by highlighting diverse applications. Topics include characterizations of convex sets, polytopes, duality, optimization, and convex functions. Exercises appear throughout the text, with solutions, hints, and references at the end. 1982 ...

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Convex Analysis and Minimization Algorithms: Part 1: Fundamentals more books like this

by Jean-Baptiste Hiriart-Urruty, Claude Lemarechal

Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to ...

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Geometric applications of Fourier series and spherical harmonics

Geometric applications of Fourier series and spherical harmonics more books like this

by Groemer

This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used ...

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Foundations of mathematical optimization convex analysis without linearity

Foundations of mathematical optimization convex analysis without linearity more books like this

by Pallaschke, Rolewicz

Many books on optimization consider only finite dimensional spaces. This volume has a different 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 ...

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Convex Analysis and Global Optimization

Convex Analysis and Global Optimization more books like this

by Tuy Hoang, Tuy Hoang Tuy

Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes ...

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Abstract Convex Analysis

Abstract Convex Analysis more books like this

by Ivan Singer

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.

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Convex Analysis and Minimization Algorithms I

Convex Analysis and Minimization Algorithms I more books like this

by Jean-Baptiste Hiriart-Urruty, Claude Lemarechal

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Non-Connected Convexities and Applications

Non-Connected Convexities and Applications more books like this

by Gabriela Cristescu, Liana Lupsa

The notion of convex set, known according to its numerous applications in linear spaces due to its connectivity which leads to separation and support properties, does not imply, in fact, necessarily, the connectivity. This aspect of non-connectivity hidden under the convexity is discussed in this book. The property of non-preserving the ...

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Convex Analysis and Minimization Algorithms: Part 2: Advanced Theory and Bundle Methods more books like this

by Jean-Baptiste Hiriart-Urruty, Claude Lemarechal

The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations...one of the strong features of these books...that they are designed not for the expert, but for those who wish to learn the subject matter ...

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Geometric Aspects of Convex Sets with the Radon-Nikodym Property more books like this

by R D Bourgin

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Discrete Convex Analysis more books like this

by Kazuo Murota

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development ...

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Convex sets more books like this

by Frederick A. Valentine

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Integer Points in Polyhedra: Geometry, Number Theory, Algebra, Optimization: Proceedings of an Ams-IMS-Siam Joint Summer Research Conference on Integer Points in Polyhedra, Geometry, Number Theory, Algebra, Optimization, July 13-17, 2003, Snowbird, Utah more books like this

by Alexander Barvinok

The AMS-IMS-SIAM Summer Research Conference on Integer Points in Polyhedra took place in Snowbird (UT). This proceedings volume contains original research and survey articles stemming from that event. Topics covered include commutative algebra, optimization, discrete geometry, statistics, representation theory, and symplectic geometry. The book is ...

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Compact Convex Sets and Boundary Integrals more books like this

by Erik Magnus Alfsen

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Geometric Functional Analysis and Its Applications more books like this

by Richard B. Holmes

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Fourier Analysis in Convex Geometry more books like this

by Alexander Koldobsky

The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use ...

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Convexity, Theory & Its Application in Functional Analysis more books like this

by L Asimow, A J Ellis

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Integer Points in Polyhedra more books like this

by Alexander Barvinok

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Convexity and its applications more books like this

by Peter M. Gruber, Jörg M. Wills

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Pairs of Compact Convex Sets: Fractional Arithmetic with Convex Sets more books like this

by Diethard Pallaschke, M I Ursul, Ryszard Urbanski

The book is devoted to the theory of pairs of compact convex sets and, in particular, to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Radstrom-Hormander Theory. Minimal pairs of compact convex sets arise naturally in different ...

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Blaschke's Rolling Theorem in RN more books like this

by J. Brooks, J. Strantzen

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Konvexe Analysis more books like this

by Jürg T. Marti

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