Recent Developments in Vector Optimization

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Qamrul Hasan Ansari, Jen-Chih Yao
Springer Science & Business Media, Sep 21, 2011 - Business & Economics - 552 pages
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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.
 

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Contents

Vector Optimization Problems and Their Solution Concepts
1
GordanType Alternative Theorems and Vector Optimization Revisited
29
Duality in Vector Optimization with Infimum and Supremum
60
Variable Ordering Structures in Vector Optimization
95
Strong KKT Second Order Conditions and Nonsolid Cones in Vector Optimization
127
Optimality Conditions and Image Space Analysis for Vector Optimization Problems
169
Nonsmooth Invexities Invariant Monotonicities and Nonsmooth Vector VariationalLike Inequalities with Applications to Vector Optimization
221
Optimality Conditions for Approximate Solutions of Convex SemiInfinite Vector Optimization Problems
275
Linear Fractional and Convex Quadratic Vector Optimization Problems
296
LevitinPolyak Type WellPosednessin Constrained Optimization
329
Vector Variational Principles for SetValued Functions
367
The Fermat Rule and Lagrange Multiplier Rule for Various Efficient Solutions of SetValued Optimization Problems Expressed in Terms of Coderivat...
416
Extended Pareto Optimality in Multiobjective Problems
467
Vector Optimization and Cooperative Games
517
Index
546
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