Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces
Keywords:
Vector optimization, relatively solid convex cones, intrinsic core, minimality, efficiency, weak duality, strong duality, regularity.Abstract
We derive duality assertions for vector optimization problems in real linear spaces based on a scalarization using recent results concerning the concept of relative solidness for convex cones (i.e., convex cones with nonempty intrinsic cores). In our paper, we consider an abstract vector optimization problem with generalized inequality constraints and investigate Lagrangian type duality
assertions for (weak, proper) minimality notions. Our interest is neither to impose a pointedness assumption nor a solidness assumption for the convex cones involved in the solution concept of the vector optimization problem. We are able to extend the well-known Lagrangian vector duality approach by J.Jahn [Duality in vector optimization, Math. Programming 25 (1983) 343–353] to
such a setting
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