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7 edition of Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics) found in the catalog.

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

## by Ivan Singer

Written in English

The Physical Object
Number of Pages356
ID Numbers
Open LibraryOL7445070M
ISBN 100387283943
ISBN 109780387283944

Duality in Problems Governed by Polyhedral Maps. Duality in Problems Described by Convex Discrete Inclusions. The Main Duality Results in Problems with Convex Differential Inclusions. 6. Optimization of Discrete and Differential Inclusions with Distributed Parameters via . CMS Books in Mathematics is a collection of advanced books and monographs published in cooperation with Springer since This series offers authors the joint advantage of publishing with a major mathematical society and with a leading academic publishing company. Duality for Nonconvex Approximation and Optimization I., ISBN

This article presents an approach to generalized convex duality theory based on Fenchel-Moreau conjugations; in particular, it discusses quasiconvex conjugation and duality in detail. and applications to approximation, Optimization 45, pp. – () Duality in nonconvex optimization, J. Math. Anal. Appl. 66, pp. – ().Cited by: Canonical dual solutions to nonconvex radial basis neural network optimization problem. Author links open overlay panel Vittorio Latorre a David Yang Gao b c. We have presented a concrete application of the canonical duality theory to function approximation using Radial Basis axendadeportiva.com by:

Amir Beck and Aharon Ben-Tal On the Solution of the Tikhonov Regularization of the Total Least Squares, SIAM J. Optimization, 17(1): (). Amir Beck and Yonina C. Eldar Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints SIAM . Oct 14,  · Book Review Book Review BOOK REVIEW sets, the study of d.c. structures is very important for the design of efﬁcient so- lution methods for these problems. More speciﬁc results concerning duality and partitioning (decomposition) on the d.c. structure are also discussed. Based on the previous part, Part II, entitled ‘Methods and Algorithms’, is de- voted to.

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### Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics) by Ivan Singer Download PDF EPUB FB2

Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics Book 24) - Kindle edition by Ivan Singer. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics Book 24).Manufacturer: Springer New York.

In this monograph the author presents the theory of duality for. nonconvex approximation in normed linear spaces and nonconvex global. optimization in locally convex spaces. Key topics include: * duality for worst approximation (i.e., the maximization of the.

distance of an element to a convex set). In this monograph the author presents the theory of duality for. nonconvex approximation in normed linear spaces and nonconvex global. optimization in locally convex spaces. Key topics include: * duality for worst approximation (i.e., the maximization of the.

distance of an element to a convex set)Author: Ivan Singer. Feb 28,  · Duality for Nonconvex Approximation and Optimization by Ivan Singer,available at Book Depository with free delivery worldwide.

Get this from a library. Duality for nonconvex approximation and optimization. [Ivan Singer] -- "In this monograph the author presents the theory of duality for nonconvex approximation in normed linear spaces and nonconvex global optimization in locally convex spaces.

Key topics include: *. Get this from a library. Duality for nonconvex approximation and optimization. [Ivan Singer] -- "In this monograph the author presents the theory of duality for nonconvex approximation in normed linear spaces and nonconvex global optimization in locally convex spaces.

Detailed proofs of results. Duality for Quasi-convex Supremization.- Optimal Solutions for Quasi-convex Maximization.- Reverse Convex Best Approximation.- Unperturbational Duality for Reverse Convex Infimization.- Optimal Solutions for Reverse Convex Infimization.- Duality for D.C.

Optimization Problems.- Duality for Optimization in the Framework of Abstract Convexity duality for nonconvex approximation and optimization cms books in mathematics Dec 10, Posted By Evan Hunter Media TEXT ID Online PDF Ebook Epub Library professor kaplan the most duality concepts which can be found in the literature on vector optimization this book being no exception have the origin in well developed.

The duality gap is zero if and only if strong duality holds. Otherwise the gap is strictly positive and weak duality holds. In computational optimization, another "duality gap" is often reported, which is the difference in value between any dual solution and the value of.

Given a locally convex space X, with conjugate space X *, a convex subset G of X, and a function ƒ: X → $$\bar R$$, in this chapter we shall give some results of unperturbational duality for the primal “reverse convex infimization” problem.

Welcome to the Northwestern University Process Optimization Open Textbook. This electronic textbook is a student-contributed open-source text covering a variety of topics on process optimization. If you have any comments or suggestions on this open textbook, please contact Professor Fengqi You.

Convex optimization is one of the main applications of the theory of convexity and Legendre–Fenchel duality is a basic tool, making more flexible the approach of many concrete problems.

articles [15, 27] and the newly published book [23] provide comprehensive reviews and applications of the canonical duality theory in multidisciplinary elds of mathematical modeling, engineering mechanics, nonconvex analysis, global optimization, and computational science.

The most duality concepts which can be found in the literature on vector optimization, this book being no exception, have the origin in well-developed duality theories for scalar problems.

Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints. Related Databases. a safe tractable approximation approach.

IET Communications() Hidden Convexity in QCQP with Toeplitz-Hermitian Quadratics. Cited by: A duality with zero gap for nonconvex optimization problems is presented.

The first class of nonconvex problems, where local optima may not be global, is a quasi-convex minimization over a convex set. For this class a generalized Kuhn–Tucker condition is obtained, and the duality is similar to the Fenchel–Moreau–Rockafellar duality axendadeportiva.com by: Conjugate Duality and Optimization R.

Tyrrell Rockafellar 1. The role of convexity and duality. In most situations involving optimiza-tion there is a great deal of mathematical structure to work with. However, in order to get to the fundamentals, it is convenient for us to begin by considering.

This book provides an up-to-date, comprehensive, and rigorous account of nonlinear programming at the first year graduate student level. It covers descent algorithms for unconstrained and constrained optimization, Lagrange multiplier theory, interior point and augmented Lagrangian methods for linear and nonlinear programs, duality theory, and major aspects of large-scale optimization.

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex axendadeportiva.com classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and. Nonconvex Generalized Benders Decomposition It is very difﬁcult to obtain optimal dual solution for a nonconvex primal!.

Duality gap. Convex relaxation gap. 11 Nonconvex Generalized Benders Decomposition: Overview Applied to hard nonconvex optimization problems in optimal. This number is used to estimate the duality gap in optimization problems where the criterion and/or the constraints are nonconvex.

It is shown that when the number of variables is very great with respect to the number of constraints, this duality gap is small in relative axendadeportiva.com by: This book aims at an up-to-date and accessible development of algorithms for solving convex optimization problems.

The book covers almost all the major classes of convex optimization algorithms. Principal among these are gradient, subgradient, polyhedral approximation, proximal, and .However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a mini­ mum as a zero duality gap is not always guaranteed.

A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those.