159. Henig Proper Efficient Points: Existence and Density Beyond Convexity
Invited abstract in session TC-9: Variational Analysis II, stream Variational analysis: theory and algorithms.
Tuesday, 14:00-16:00Room: B100/8013
Authors (first author is the speaker)
| 1. | Fernando García Castaño
|
| Mathematics, University of Alicante | |
| 2. | Miguel Angel Melguizo Padial
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| Mathematics, University of Alicante |
Abstract
In this talk, we present new results on the existence and density of Henig global proper efficient points in vector optimization problems within arbitrary normed spaces. Our approach does not require convexity and, in some cases, applies to unbounded sets. However, a weak compactness condition --either on the set or a section of it-- remains essential, along with a key separation property between the order cone and its conical neighborhoods. These conditions ensure the necessary convergence properties and allow the interpolation of a family of Bishop-Phelps cones between the order cone and its neighborhoods. This interpolation, together with a careful interaction between two types of conic neighborhoods, plays a fundamental role in our proofs. Our results generalize some existing results in the literature that were obtained under more restrictive assumptions.
Keywords
- Linear and nonlinear optimization
- Non-smooth optimization
- Conic and semidefinite optimization
Status: accepted
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