Download or read book A New Approach to Duality in Vector Optimization written by Andreas Löhne and published by . This book was released on 2005 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Optimization and Monotone Operators via Convex Duality written by Sorin-Mihai Grad and published by Springer. This book was released on 2014-09-03 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Duality in Vector Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-08-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Vector Optimization with Infimum and Supremum written by Andreas Löhne and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
Download or read book GEOMETRIC APPROACH TO ISERMAN DUALITY IN LINEAR VECTOR OPTIMIZATION written by Hirotaka Nakayama and published by . This book was released on 1986 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.
Download or read book Optimization by Vector Space Methods written by David G. Luenberger and published by John Wiley & Sons. This book was released on 1997-01-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Download or read book Theory of Vector Optimization written by Dinh The Luc and published by Springer. This book was released on 1989 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic study of the most important topics of vector optimization such as the existence of efficient points, optimality conditions, scalarization, duality, and the structure of optimal solutions sets. New methods to which particular attention is paid are the theory of nonconvex analysis or analysis over cones, the theory of contingent derivatives of set-valued maps, and the nonstandard approach to duality. By reading this book, graduate students can easily comprehend basic concepts and the most important methods of vector optimization. The researchers who are familiar with this theory will find in the book several new approaches to the subject together with the latest results on it.
Download or read book Recent Developments in Vector Optimization written by Qamrul Hasan Ansari and published by Springer Science & Business Media. This book was released on 2011-09-21 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.
Download or read book Conjugate Duality in Convex Optimization written by Radu Ioan-Bot and published by Springer. This book was released on 2011-03-03 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.
Download or read book Duality in Optimization and Variational Inequalities written by C.j. Goh and published by Taylor & Francis. This book was released on 2002-05-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book On Lagrangian Duality in Vector Optimization written by Elisa Pagani and published by . This book was released on 2015 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: We recall a general scheme for vector problems based on separation arguments and alternative theorems, and then, this approach is exploited to study Lagrangian duality in vector optimization.We show that the vector linear duality theory due to Isermann can be embedded in this separation approach. The theoretical part of this paper serves the purpose of introducing two possible applications. Some well-known classical applications in economics are the minimization of costs and the maximization of profit for a firm. We extend these two examples to the multiobjective framework in the linear case, exploiting the duality theory of Isermann. For the former, we consider the minimization of costs and of pollution as two different and conflicting goals; for the latter, we introduce as second objective function the profit for a competitor firm. This allows us to study the relationships between the shadow prices referred to the two different goals and to introduce a new representation of the feasible region of the dual problem.
Download or read book Vector Optimization written by Johannes Jahn and published by Springer Science & Business Media. This book was released on 2010-11-22 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Set Optimization and Applications The State of the Art written by Andreas H Hamel and published by Springer. This book was released on 2015-11-21 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents five surveys with extensive bibliographies and six original contributions on set optimization and its applications in mathematical finance and game theory. The topics range from more conventional approaches that look for minimal/maximal elements with respect to vector orders or set relations, to the new complete-lattice approach that comprises a coherent solution concept for set optimization problems, along with existence results, duality theorems, optimality conditions, variational inequalities and theoretical foundations for algorithms. Modern approaches to scalarization methods can be found as well as a fundamental contribution to conditional analysis. The theory is tailor-made for financial applications, in particular risk evaluation and [super-]hedging for market models with transaction costs, but it also provides a refreshing new perspective on vector optimization. There is no comparable volume on the market, making the book an invaluable resource for researchers working in vector optimization and multi-criteria decision-making, mathematical finance and economics as well as [set-valued] variational analysis.
Download or read book Set valued Optimization written by Akhtar A. Khan and published by Springer. This book was released on 2014-10-20 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.
Download or read book A New Duality Approach for Multiobjective Convex Optimization Problems written by Radu Ioan Boţ and published by . This book was released on 2001 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
