8 edition of **Duality in optimization and variational inequalities** found in the catalog.

- 71 Want to read
- 9 Currently reading

Published
**2002** by Taylor & Francis in London, New York .

Written in English

- Duality theory (Mathematics),
- Mathematical optimization.

**Edition Notes**

Includes bibliographical references (p. 293-302) and index.

Statement | C.J. Goh and X.Q. Yang. |

Series | Optimization theory and applications ;, v. 2 |

Contributions | Yang, Xiaoqi. |

Classifications | |
---|---|

LC Classifications | QA564 .G615 2002 |

The Physical Object | |

Pagination | xvi, 313 p. : |

Number of Pages | 313 |

ID Numbers | |

Open Library | OL3434302M |

ISBN 10 | 0415274796 |

LC Control Number | 2005274958 |

Using duality, we reformulate the asymmetric variational inequality (VI) problem over a conic region as an optimization problem. We give sufficient conditions for the convexity of this reformulation. We thereby identify a class of VIs that includes monotone affine VIs over polyhedra, which may be solved by commercial optimization solvers. Vector Variational Inequality and Vector Pseudolinear Optimization Problems. Introduction. Vector Variational Inequality Problems. Necessary and Sufficient Optimality Conditions. Nonsmooth Vector Variational Inequality Problems. Necessary and Sufficient Optimality Conditions. Extension of Pseudolinear Functions and Variational Inequality. [10] C. S. Lalitha and M. Mehra: Vector variational inequalities with cone-pseudomonotone bifunction, Optim., 54(), [11] U. Mosco: Implicit variational methods and quasi variational inequalities, in: Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Germany, (),

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Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different by: Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality.

It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

Mathematical Preliminaries 2. Duality in Network Optimization 3. Duality in Linear Systems 4. Duality in Convex Nonlinear Systems 5. Duality in Nonconvex Systems 6. Duality in Variational Inequalities 7.

Elements of Multicriteria Optimization 8. Duality in Multicriteria Optimization 9. Duality in Vector Variational Inequalities: Series Title. Stampacchia,” the International Workshop on Optimization and Control with Applications.

The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation; and.

On Duality for Extended Monotropic Optimization and Application to the In nite Sum of Functions coffee break G. Crespi Set-optimization and variational analysis: new perspectives and challenges D. Aussel Existence results for variational inequalities: recent advances lunchFile Size: KB.

Developing a simple Lagrangian duality scheme which is combined with the recent logarithmic-quadratic proximal (LQP) theory introduced by the authors, we derive three algorithms for solving the variational inequality (VI) by: This book is a concise account of convex analysis, its applications and extensions, for a broad audience.

Blurring as it does the distinctions between mathematical optimization and modern analysis, the elegant language of convexity and duality is indispensable both in computational optimization and for understanding variational properties of. 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. Progressive decoupling of linkages in monotone variational inequalities and convex optimization, in Proceedings of the 10th International Conference on Nonlinear Analysis and Convex Analysis (Chitose, JapanmYokohama Publishers, Japan (by R.

Rockafellar). The purpose of this book is to provide a systematic and comprehensive account of asymptotic sets and functions, from which a broad and u- ful theory emerges in the areas of optimization and variational inequa- ties.

There is a variety of motivations. OPTIMIZATION and VARIATIONAL INEQUALITIES Basic statements and constructions @ ; May Abstract. This paper summarizes basic facts in both nite and in nite dimensional optimization and for variational inequalities. In addition, partially new results (concerning methods Existence of solutions, (strong) duality.

Jadamba is affiliated with the School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York. Her primary research interest is in uncertainty quantification in network models, variational inequalities, and inverse problems.

She has published more than 30 scientific papers. functions for the primal and dual variational inequality problems.

They related the problems with the help of dual Fenchel optimization problems. It was also pointed out by Chen, Goh and Yang [3] that to understand the duality of variational inequality problems initsfull generality, itismoreexpedienttostudy theextended variational inequality.

A duality approach to gap functions for variational inequalities and equi-librium problems Dissertation, pages, Chemnitz University of Technology, Faculty of 2 Variational inequalities and equilibrium problems 23 been associated to the Lagrange duality for optimization problems.

In order to. Using duality, we reformulate the asymmetric variational inequality (VI) problem over a conic region as an optimization problem. We give sufficient conditions for the convexity of this Author: Michele Aghassi.

Key words: Vector variational inequality, gap functions, duality, Fenchel conjugate. 2 1 Introduction The concept of a gap function is well-known both in the context of convex optimization (Hearn.

Browse Books. Home Browse by Title Progressive Regularization of Variational Inequalities and Decomposition Algorithms, Journal of Optimization Theory and Applications,(), Online publication date: 1-May Cohen G () An algorithm for convex constrained minimax optimization based on duality, Applied Mathematics and.

THEORETICAL BACKGROUND M(w) operators (see Pazy [2]) Let E be a real Hilbert space and w a real number. A multivalued operator G in E is called a maximal-M(w) operator if G + wl is maximal monotone.

Duality methods for solving variational inequalities 45 If Aw Cited by: () A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework.

Optimization Methods and Software() Extended auxiliary problem principle to variational inequalities involving multi-valued by: We consider a new class of multiplier interior point methods for solving variational inequality problems with maximal monotone operators and explicit convex constraint inequalities.

Developing a simple Lagrangian duality scheme which is combined with the recent logarithmic-quadratic proximal (LQP) theory introduced by the authors, we derive. We propose a robust optimization approach to analyzing three distinct classes of problems related to the notion of equilibrium: the nominal variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand by: 3.

FENCHEL DUALITY THEORY AND A PRIMAL-DUAL ALGORITHM ON RIEMANNIAN MANIFOLDS RONNY BERGMANN y, ROLAND HERZOG, DANIEL TENBRINCKz, AND book on optimization on matrix manifolds, seeAbsil, Mahony, Sepulchre, Cis strongly convex), we still have a generalization of the classical variational inequality which characterizes certain solutions Author: Ronny Bergmann, Roland Herzog, Daniel Tenbrinck, José Vidal-Núñez.

Daniele, Variational inequalities for static equilibrium market. Lagrangian function and duality, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models, eds. Giannessi, A. Maugeri and P. Pardalos (Kluwer, ) pp. 43– Google ScholarCited by: In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set.

The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems. Publisher Summary. Convex sets and convex functions are studied in this chapter in the setting of n-dimensional Euclidean space R ity is an attractive subject to study, for many reasons; it draws upon geometry, analysis, linear algebra, and topology, and it has a role to play in such topics as classical optimal control theory, game theory, linear programming, and convex programming.

This book provides a systematic and comprehensive account of asymptotic sets and functions from which a broad and useful theory emerges in the areas of optimization and variational inequalities. A variety of motivations lead mathematicians to study questions revolving around attainment of the infimum in a minimization problem and its stability.

Books. Boţ () - Conjugate Duality in Convex Optimization, Lecture Notes in Economics and Mathematical Systems, Vol.Springer-Verlag Berlin Heidelberg ; R. Boţ, S. Grad, G. Wanka () - Duality in Vector Optimization, Springer-Verlag Berlin Heidelberg ; Articles.

Boţ, E. Csetnek, P.T. Vuong - The forward-backward-forward method from continuous and discrete. Using duality, we reformulate the asymmetric variational inequality (VI) problem over a conic region as an optimization problem. We give sufﬁcient conditions for the convexity of this reformulation. We thereby identify a class ofVIs that includes monotone afﬁne VIs over polyhedra, which may be solved by commercial optimization solvers.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We present a scheme which associates to a generalized quasi-variational inequality a dual problem and generalized Kuhn-Tucker conditions.

This scheme allows to solve the primal and the dual problems in the spirit of the classical Lagrangian duality for constrained optimization problems and extends, in non necessarily.

This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization.

Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are : Akhtar A. Khan, Elisabeth Köbis, Christiane Tammer. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension).

It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a. Duality (optimization) 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 problem.

The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. Particularly, a special case is considered, where the players' optimization problems are linear at both stages, and it is shown that the Nash equilibrium of this game can be obtained by solving a conic linear variational inequality by: 2.

Generalized Convexity and Generalized Monotonicity: Optimality and Wolfe Duality for Multiobjective Programming Problems Involving nset Functions.

semidefinite sequence solving Steiner ratio stochastic order subdifferential supermodular Suppose supremum Theorem theory tions variational inequality vector optimization. The aim of this paper is to extend the so-called perturbation approach in order to deal with conjugate duality for constrained vector optimization problems.

To this end we use two conjugacy notions introduced in the past in the literature in the. This paper deals with an application of duality theory in optimization to the construction of gap functions for quasi-variational inequalities. The same approach was investigated for variational inequalities and equilibrium problems in (Pac.

Optim. 2(3):; Asia-Pac. Oper. Res. 24(3):), and the study shows that we can obtain some previous results for variational Cited by: 1. VARIATIONAL INEQUALITY AND EQUILIBRIUM - Chapter Decomposable Generalized Vector Variational Inequalities - Chapter On a Geometric Lemma and Set-Valued Vector Equilibrium Problem - Chapter Equilibrium Problems - Chapter Gap Functions and Descent Methods for Minty Variational Inequality - Chapter This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization.

Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities.

Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be :. This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces.

non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers.We also show that (i) and (ii) can basically be interpreted as weak duality and strong duality respectively.

Lastly, we show that the gap functions of a pair of primal-dual variational inequality corresponds to a pair of primal-dual Fenchel optimization problems. 2. Duality of Variational Inequality.The application of variational inequalities to free-boundary problems arising in the flow of fluids through porous media was studied by Baiocchi[l3] and Baiocchi et al.[14], and a numerical analysis of such problems was investigated by Baiocchi et al.

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