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| Author | : Sorin-Mihai Grad |
| Publisher | : |
| Total Pages | : 18 |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
| Author | : Radu Ioan Bot |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 408 |
| Release | : 2009-08-12 |
| Genre | : Mathematics |
| ISBN | : 3642028861 |
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.
| Author | : Johannes Jahn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 409 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 3642466184 |
In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.
| Author | : Johannes Jahn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 490 |
| Release | : 2010-11-22 |
| Genre | : Business & Economics |
| ISBN | : 3642170056 |
Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning. This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.
| Author | : Sorin-Mihai Grad |
| Publisher | : Springer |
| Total Pages | : 282 |
| Release | : 2014-09-03 |
| Genre | : Business & Economics |
| ISBN | : 3319089005 |
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
| Author | : C.j. Goh |
| Publisher | : Taylor & Francis |
| Total Pages | : 344 |
| Release | : 2002-05-10 |
| Genre | : Mathematics |
| ISBN | : 9780415274791 |
This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. 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.
| Author | : Qamrul Hasan Ansari |
| Publisher | : Springer |
| Total Pages | : 517 |
| Release | : 2017-10-31 |
| Genre | : Business & Economics |
| ISBN | : 3319630490 |
This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
| Author | : Ivan Singer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 366 |
| Release | : 2007-03-12 |
| Genre | : Mathematics |
| ISBN | : 0387283951 |
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.
| Author | : R. Tyrrell Rockafellar |
| Publisher | : SIAM |
| Total Pages | : 82 |
| Release | : 1974-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 0898710138 |
The theory of duality in problems of optimization is developed in a setting of finite and infinite dimensional spaces using convex analysis. Applications to convex and nonconvex problems. Expository account containing many new results. (Author).
| Author | : Johannes Jahn |
| Publisher | : Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften |
| Total Pages | : 330 |
| Release | : 1985-12-31 |
| Genre | : Mathematics |
| ISBN | : |
In vector optimization one investigates optimal elements such as minimal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The problem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineering and economics. Vector optimization problems arise, for example, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multi-objective programming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems).
