EUROPT 2025
Abstract Submission

19. Local Upper Bounds for General Ordering Cones

Invited abstract in session WB-10: Global Multi-Objective Optimization, stream Multiobjective and Vector Optimization.

Wednesday, 10:30-12:30
Room: B100/8011

Authors (first author is the speaker)

1. Gabriele Eichfelder
Institute of Mathematics, Technische Universität Ilmenau
2. Firdevs Ulus
Industrial Engineering, Bilkent University

Abstract

The concept of local upper bounds plays an important role for numerical algorithms in nonconvex, integer, and mixed-integer multiobjective optimization with respect to the componentwise partial ordering, that is, where the ordering cone is the nonnegative orthant. In this talk, we answer the question on whether and how this concept can be extended to arbitrary ordering cones. This question has frequently arisen after talks, and this presentation aims to provide a comprehensive answer. We define local upper bounds with respect to a closed pointed solid convex cone and study their properties. We show that for special polyhedral ordering cones the concept of local upper bounds can be as practical as it is for the nonnegative orthant.

Keywords

Status: accepted


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