Annotation 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 Vector optimization problems and their solution concepts / Gabriele Eichfelder and Johannes Jahn Gordan-type alternative theorems and vector optimization revisited / Fabiâan Flores-Bazâan, Fernando Flores-Bazâan, and Cristiâan Vera Duality in vector optimization with infimum and supremum / Andreas Lèohne Variable ordering structures in vector optimization / Gabriele Eichfelder Strong KKT, second order conditions and non-solid cones in vector optimization / Joydeep Dutta Optimality conditions and image space analysis for vector optimization problems / Giandomenico Mastroeni Nonsmooth invexities, invariant monotonicities and nonsmooth vector variational-like inequalities with applications to vector optimization / Suliman Al-Homidan, Qamrul Hasan Ansari, and Jen-Chih Yao Optimality conditions for approximate solutions of convex semi-infinite vector optimization problems / Gue Myung Lee, Gwi Soo Kim, and Nguyen Dinh Linear fractional and convex quadratic vector optimization problems / Nguyen Dong Yen Levitin-Polyak type well-posedness in constrained optimization / Xue-Xiang Huang Vector variational principles for set-valued functions / Christiane Tammer and Constantin Zæalinescu The Fermat Rule and Lagrange Multiplier Rule for various efficient solutions of set-valued optimization problems expressed in terms of coderivatives / Truong Xuan Duc Ha Extended Pareto optimality in multiobjective problems / Truong Q. Bao and Boris S. Mordukhovich Vector optimization and cooperative games / Tetsuzo Tanino. Front Matter....Pages i-xxiv Vector Optimization Problems and Their Solution Concepts....Pages 1-27 Gordan-Type Alternative Theorems and Vector Optimization Revisited....Pages 29-59 Duality in Vector Optimization with Infimum and Supremum....Pages 61-94 Variable Ordering Structures in Vector Optimization....Pages 95-126 Strong KKT, Second Order Conditions and Non-solid Cones in Vector Optimization....Pages 127-167 Optimality Conditions and Image Space Analysis for Vector Optimization Problems....Pages 169-220 Nonsmooth Invexities, Invariant Monotonicities and Nonsmooth Vector Variational-Like Inequalities with Applications to Vector Optimization....Pages 221-274 Optimality Conditions for Approximate Solutions of Convex Semi-Infinite Vector Optimization Problems....Pages 275-295 Linear Fractional and Convex Quadratic Vector Optimization Problems....Pages 297-328 Levitin–Polyak Type Well-Posedness in Constrained Optimization....Pages 329-365 Vector Variational Principles for Set-Valued Functions....Pages 367-415 The Fermat Rule and Lagrange Multiplier Rule for Various Efficient Solutions of Set-Valued Optimization Problems Expressed in Terms of Coderivatives....Pages 417-466 Extended Pareto Optimality in Multiobjective Problems....Pages 467-515 Vector Optimization and Cooperative Games....Pages 517-545 Back Matter....Pages 547-551
