Last edited by Meztishicage
Monday, May 4, 2020 | History

5 edition of Duality principles in nonconvex systems found in the catalog.

# Duality principles in nonconvex systems

## by David Yang Gao

Written in English

Subjects:
• Mathematical optimization.,
• Convex programming.,
• Duality theory (Mathematics)

• Edition Notes

Includes bibliographical references (p. 433-448) and index.

Classifications The Physical Object Statement by David Yang Gao. Series Nonconvex optimization and its applications -- v. 39 LC Classifications QA402.5 .G29 2000 Pagination xviii, 454 p. : Number of Pages 454 Open Library OL21801100M ISBN 10 0792361458 LC Control Number 99088585

Abstract: This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual variational formulation and such an approach includes optimality conditions which guarantee zero duality gap between the primal and dual : Fabio Botelho. A general duality theory is given for smooth nonconvex optimization problems, covering both the finite-dimensional case and the calculus of variations. The results are quite similar to the convex case; in particular, with every problem $(\mathcal{P})$ is associated a dual problem $(\mathcal{P}^ * Cited by: Abstract Convexity for Nonconvex Optimization Duality Angelia Nedic⁄, Asuman Ozdaglar y, and Alex Rubinov z Febru Abstract In this paper, we use abstract convexity results to study augmented dual prob-lems for (nonconvex) constrained optimization problems. We consider a nonin-. Duality Principles in Nonconvex Systems: Theory, Methods and Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth. Abstract. Abstract. This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + pp], the nonconvex Cited by: Comments on \Dual Methods for Nonconvex Spectrum Optimization of Multicarrier Systems" Tam as Terlaky and Jiaping Zhuy July 5, Abstract Yu and Liu’s strong duality theorem under the time-sharing property requires the Slater condition to hold for the considered general nonconvex problem, what is satis ed for the speci c application. Available for Download Share this book You might also like Inspecting the manufacture of sterile products Inspecting the manufacture of sterile products Autophagy in Immunity And Infection Autophagy in Immunity And Infection This is the Agency for Agricultural Research and Development (AARD) This is the Agency for Agricultural Research and Development (AARD) Meat Inspector-Poultry Inspector Meat Inspector-Poultry Inspector Poetreat Poetreat CALISCE 94 CALISCE 94 Professional Ethics and Law in the Health Sciences Professional Ethics and Law in the Health Sciences Australian Children Through 200 Years Australian Children Through 200 Years Interstate Stalking Punishment and Prevention Act of 1996 Interstate Stalking Punishment and Prevention Act of 1996 Mortality and crisis mortality in eighteenth century Mexico Mortality and crisis mortality in eighteenth century Mexico Roachs beauties of the poets. Cymon and Iphigenia, by John Dryden. Morning and evening, by Dr. Gregory. Lallegro, by John Milton. The cits country box, by Robert Lloyd. The first of April, by Thomas Warton. The negro boy, by Mr. Samwell Roachs beauties of the poets. Cymon and Iphigenia, by John Dryden. Morning and evening, by Dr. Gregory. Lallegro, by John Milton. The cits country box, by Robert Lloyd. The first of April, by Thomas Warton. The negro boy, by Mr. Samwell ### Duality principles in nonconvex systems by David Yang Gao Download PDF EPUB FB2 Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering by: Duality Principles in Nonconvex Systems: Theory, Methods and Applications (Nonconvex Optimization and Its Applications (39)) Softcover reprint of hardcover 1st ed. Edition by David Yang Gao (Author) › Visit Amazon's David Yang Gao Page. Find all the books, read about the author, and more. Cited by: From traditional convex systems to general nonlinear systems, we will study, in this chapter, the generalized duality theory and analytic solutions for one-dimensional nonconvex variational Author: David Yang Gao. Get this from a library. Duality Principles in Nonconvex Systems: Theory, Methods and Applications. [David Yang Gao] -- Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a. Offers a comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. This book covers topics such as the classical (minimax) mono-duality of convex static equilibria, the bi-duality in dynamical systems, and the tri-duality in non-convex problems. Book Review: David Yang Gao, Duality Principles in Nonconvex Systems. Theory, Methods and Applications. Abstract. In this chapter we shall select topics from finite deformation continuum mechanics and minimum surface type problems in differential geometry, and use them to illustrate a general duality theory for n-dimensional nonconvex finite deformation systems in which the geometrical mapping Λ is a nonlinear partial differential methods and ideas can certainly be generalized to Author: David Yang Gao. Duality Principles in Nonconvex Systems: Theory, Methods and Applications, Vol. xviii, p. Kluwer Academic Publishers, Dordrecht/Boston/London.]. Several examples are illustrated including the Author: David Yang Gao. In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However in general the optimal values of the primal and dual problems need not be equal. The duality theory concerns itself with the relationship between the primal and the dual problems. In principle one can inquire for any optimization problem, convex or not, whether there is a dual problem associated with it. In a recent paper [2], a notion of duality for Cited by: In this paper, by providing simple counterexamples, several important results in bi-duality, triality and tri-duality, an optimization theory established and presented by D.Y. Gao in his book "Duality Principles in Nonconvex Systems. Theory, Methods and Applications," Kluwer Academic Publishers, Dordrecht,are proven to be by: Springer, p. Nonconvex Optimization and Its Applications ISBN Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained. Nonconvex Optimization and Variational Problem 89 Commentary 94 Part II Symmetry Breaking: Triality Theory in Nonconvex Systems 3. TRI-DUALITY IN NONCONVEX SYSTEMS 99 Constitutive Symmetry Breaking in Convex Systems Legendre Duality Breaking: KKT conditions Duality Restoration: Finite Deformation Measures applications in structural limit analysis [32, 33]. However, the one-to-one duality is bro-ken in nonconvex systems. In large deformation theory, the stored energy is generally nonconvex and its Legendre conjugate can’t be uniquely determined. It turns out that the existence of a pure stress-based complementary-dual energy principle (no duality. The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and. Discover Book Depository's huge selection of David Yang Gao books online. Free delivery worldwide on over 20 million titles. Canonical Duality Theory: Connections between Nonconvex Mechanics and Global Optimization Dedicated to Professor Gilbert Strang on the occasion of his 70th birthday David Y. Gao and Hanif D. Sherali Summary. This chapter presents a comprehensive review and some new developments on canonical duality theory for nonconvex systems. Based on. Abstract. This paper presents an application of the canonical duality theory for box constrained nonconvex and nonsmooth optimization problems. By use of the canonical dual transformation method, which is developed recently, these very difficult constrained optimization problems in can be converted into the canonical dual problems, which can be solved by deterministic : Jing Liu, Huicheng Liu. Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination Price:$. Abstract. Abstract. This paper presents a set of complete solutions to a class of polynomial optimization problems.

By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + pp], the nonconvex.David Y.

Gao is the Alex Rubinov Professor of Mathematics at the University of Ballarat and a research professor of engineering science at the Australian National University.

His research has been mainly focused on duality principles in mathematical physics and general complex systems. He has published nine books (including one monograph and one handbook) and about scientific and Cited by: Nonconvex Optimization for Communication Systems Mung Chiang Electrical Engineering Department Princeton University, Princeton, NJUSA [email protected] Summary.

Convex optimization has provided both a powerful tool and an intrigu-ing mentality to the analysis and design of communication systems over the last few years.