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Scalarization Of Approximate Solutions Of Vector Optimization Problem With Variable Order Structure Based On Nonlinear Scalarization
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Book Synopsis Scalarization of Approximate Solutions of Vector Optimization Problem with Variable Order Structure Based on Nonlinear Scalarization by : Behnam Soleimani
Download or read book Scalarization of Approximate Solutions of Vector Optimization Problem with Variable Order Structure Based on Nonlinear Scalarization written by Behnam Soleimani and published by . This book was released on 2013 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variable Ordering Structures in Vector Optimization by : Gabriele Eichfelder
Download or read book Variable Ordering Structures in Vector Optimization written by Gabriele Eichfelder and published by Springer Science & Business Media. This book was released on 2014-04-04 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.
Book Synopsis Ekeland's Variational Principle for Vector Optimization with Variable Ordering Structure by :
Download or read book Ekeland's Variational Principle for Vector Optimization with Variable Ordering Structure written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many generalizations of Ekeland's variational principle for vector optimization problems with fixed ordering structures, i.e., ordering cones. These variational principles are useful for deriving optimality conditions, epsilon-Kolmogorov conditions in approximation theory, and epsilon-maximum principles in optimal control. Here, we present several generalizations of Ekeland's variational principle for vector optimization problems with respect to variable ordering structures. For deriving these variational principles we use nonlinear scalarization techniques. Furthermore, we derive necessary conditions for approximate solutions of vector optimization problems with respect to variable ordering structures using these variational principles and the subdifferential calculus by Mordukhovich.
Book Synopsis Adaptive Scalarization Methods in Multiobjective Optimization by : Gabriele Eichfelder
Download or read book Adaptive Scalarization Methods in Multiobjective Optimization written by Gabriele Eichfelder and published by Springer Science & Business Media. This book was released on 2008-05-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.
Book Synopsis Vector Optimization Problems with Variable Ordering Structures by :
Download or read book Vector Optimization Problems with Variable Ordering Structures written by and published by . This book was released on 2015 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector optimization; Variable ordering structures; Approximate solutions; Scalarization; Separation theorems; Ekeland's variational principle; Optimality conditions
Book Synopsis Concepts of approximate solutions of vector optimization problems with variable order structure by : Behnam Soleimani
Download or read book Concepts of approximate solutions of vector optimization problems with variable order structure written by Behnam Soleimani and published by . This book was released on 2013 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Set-valued Optimization by : Akhtar A. Khan
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.
Book Synopsis Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structure by : Christiane Tammer
Download or read book Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structure written by Christiane Tammer and published by . This book was released on 2013 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A generalized scalarization method in set optimization with respect to variable domination structures by : Elisabeth Köbis
Download or read book A generalized scalarization method in set optimization with respect to variable domination structures written by Elisabeth Köbis and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce new nonlinear scalarization methods to characterize minimal elements of set-valued problems equipped with variable domination structures. For certain set relations with respect to variable domination structures, we give a characterization of these relations using corresponding nonlinear scalarizing functionals and the properties of these functionals. We describe different kinds of minimal elements to a family of sets with respect to variable domination structures. Furthermore, we investigate a descent method to find approximations of minimal solutions of set-valued problems with respect to variable domination structures using nonlinear scalarization methods. Finally, we apply the results to a set-valued problem in Medical Image Registration.
Book Synopsis Optimality Conditions for Approximate Solutions of Vector Optimization Problems with Variable Ordering Structures by : Christiane Tammer
Download or read book Optimality Conditions for Approximate Solutions of Vector Optimization Problems with Variable Ordering Structures written by Christiane Tammer and published by . This book was released on 2014 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Vector Optimization by : Guang-ya Chen
Download or read book Vector Optimization written by Guang-ya Chen and published by Springer Science & Business Media. This book was released on 2005-07-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to vector or multiple criteria approaches in optimization. Topics covered include: vector optimization, vector variational inequalities, vector variational principles, vector minmax inequalities and vector equilibrium problems. In particular, problems with variable ordering relations and set-valued mappings are treated. The nonlinear scalarization method is extensively used throughout the book to deal with various vector-related problems. The results presented are original and should be interesting to researchers and graduates in applied mathematics and operations research. Readers will benefit from new methods and ideas for handling multiple criteria decision problems.
Book Synopsis Properly Optimal Elements in Vector Optimization with Variable Ordering Structures by : Gabriele Eichfelder
Download or read book Properly Optimal Elements in Vector Optimization with Variable Ordering Structures written by Gabriele Eichfelder and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.
Book Synopsis On Nonlinear Scalarization in Vector Optimization by : Alberto Cambini
Download or read book On Nonlinear Scalarization in Vector Optimization written by Alberto Cambini and published by . This book was released on 1994 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Criteria Decision Analysis by : Salvatore Greco
Download or read book Multiple Criteria Decision Analysis written by Salvatore Greco and published by Springer. This book was released on 2016-02-18 with total page 1356 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.
Book Synopsis Set Optimization and Applications - The State of the Art by : Andreas H Hamel
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.
Book Synopsis Theory of Vector Optimization by : Dinh The Luc
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.
Book Synopsis Scalarization of Vector Optimization Problems and Properties of the Positive Cone in Normed Vector Lattices by : Richard J. Gallagher
Download or read book Scalarization of Vector Optimization Problems and Properties of the Positive Cone in Normed Vector Lattices written by Richard J. Gallagher and published by . This book was released on 1988 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
