Sublinear Scalarizations for Proper and Approximate Proper Efficient Points in Nonconvex Vector Optimization

Abstract

We show that under a separation property, a $\mathcal{Q}$-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions.

References in corpus (2)

• Denting Points of Convex Sets and Weak Property ($\pi$) of Cones in Locally Convex Spaces
• On dentability and cones with a large dual

Cited by in corpus (3)

• Existence and Density Theorems of Henig Global Proper Efficient Points
• Nonlinear Separation Theorems for Co-Radiant Sets and Optimality Conditions for Approximate and Proper Approximate Solutions in Vector Optimization
• Symmetric and Non-Symmetric Cone Separation via Bishop-Phelps Cones in Normed Spaces