38. On the convergence of outer approximation algorithms for convex vector optimization problems
Invited abstract in session TC-10: Continuous Multi-Objective Optimization: Algorithms and Complexity Analyses, stream Multiobjective and Vector Optimization.
Tuesday, 14:00-16:00Room: B100/8011
Authors (first author is the speaker)
| 1. | Firdevs Ulus
|
| Industrial Engineering, Bilkent University | |
| 2. | Cagin Ararat
|
| Industrial Engineering, Bilkent University | |
| 3. | Muhammad Umer
|
| National University of Sciences and Technology (NUST) |
Abstract
Recently in [Ç. Ararat, F. Ulus, M. Umer, SIAM Journal on Optimization, 34:3 (2024), pp 2169-3166] we studied the convergence rate of an outer approximation algorithm for solving bounded convex vector optimization problems. The algorithm solves a norm minimizing scalarization in each iteration and terminates after finitely many iterations ensuring that the Hausdorff distance between the outer approximation and the upper image is less than a given approximation error. The norm is arbitrary but fixed through the iterations. The strong convergence rate of O(k^(2/(1-q))) was proved for the Euclidean norm.
We now prove the same convergence rate for any arbitrary fixed norm. Moreover, if the norm used in the scalarization changes through the iterations, then it is possible to obtain the same convergence rate under some assumptions on the set of norms used. We show that Pascoletti-Serafini scalarization can be seen as a norm-minimizing scalarization, where the norm depends on the parameters of the scalarization.
Keywords
- Multi-objective optimization
- Global optimization
- Complexity and efficiency of algorithms
Status: accepted
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