Recent Developments in Vector Optimization
Qamrul Hasan Ansari, Jen-Chih Yao
Springer Science & Business Media, Sep 21, 2011 - Business & Economics - 552 pages
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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GordanType Alternative Theorems and Vector Optimization Revisited
Duality in Vector Optimization with Infimum and Supremum
Variable Ordering Structures in Vector Optimization
Strong KKT Second Order Conditions and Nonsolid Cones in Vector Optimization
Optimality Conditions and Image Space Analysis for Vector Optimization Problems
Nonsmooth Invexities Invariant Monotonicities and Nonsmooth Vector VariationalLike Inequalities with Applications to Vector Optimization
Optimality Conditions for Approximate Solutions of Convex SemiInfinite Vector Optimization Problems
Linear Fractional and Convex Quadratic Vector Optimization Problems
LevitinPolyak Type WellPosednessin Constrained Optimization
Vector Variational Principles for SetValued Functions
The Fermat Rule and Lagrange Multiplier Rule for Various Efficient Solutions of SetValued Optimization Problems Expressed in Terms of Coderivat...
Extended Pareto Optimality in Multiobjective Problems
Vector Optimization and Cooperative Games
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Asplund spaces Assume assumption Banach spaces coderivative compact complete lattice cone(A consider constraints convex cone convex function convex set cooperative games Corollary defined Definition denoted directional derivative dual duality efficient point equivalent exists finite function f Hence holds implies infimum intC Lagrange multiplier Lemma Let K C R linear Lipschitz LP well-posed Math minimal element minimal point monotone Mordukhovich multiobjective optimization necessary conditions necessary optimality conditions nondominated element nonsmooth normal cone notion obtain ordering cone ordering map Pareto efficient Pareto minimum partially ordered positively homogeneous Proof properly efficient solution Proposition s-efficient satisfying scalar semicontinuous sequence set-valued map set-valued optimization solution set subdifferential Theorem Theory Appl topological vector space v.m.p. of VOP variational inequality vector optimization problems vector variational inequality vector-valued w.r.t. the ordering weak Pareto weakly efficient solution well-posedness