6533b85dfe1ef96bd12bdbcb
RESEARCH PRODUCT
General duality in vector optimization
Chr. MalivertSzymon Doleckisubject
Discrete mathematicsControl and OptimizationVector operatorDual spaceApplied MathematicsDuality (optimization)Management Science and Operations ResearchVector optimizationUnit vectorOrdered vector spaceApplied mathematicsVector potentialMathematicsNormed vector spacedescription
Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x 0 ∊ A w,0 ∊ Fx$0 such that w,0 is minimal in FA. To a family of vector minimization problemsminimize , one associates a Lagrange relation where ξ belongs to an arbitrary class Ξ of mappings, the main purpose being to recover solutions of the original problem from the vector minimization of the Lagrange relation for an appropriate ξ. This ξ turns out to be a solution of a dual vector maximization problem. Characterizations of exact and approximate duality in terms of vector (generalized with respect to Ξ) convexity and subdifferentiability are given. They extend the theory existing in scalar optimization. Verifiable criteria for exact penalties are also provided
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1993-01-01 | Optimization |