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GEOMETRIC DUALITY RESULTS AND APPROXIMATION ALGORITHMS FOR CONVEX VECTOR OPTIMIZATION PROBLEMS.
- Source :
-
SIAM Journal on Optimization . 2023, Vol. 33 Issue 1, p116-146. 31p. - Publication Year :
- 2023
-
Abstract
- We study geometric duality for convex vector optimization problems. For a primal problem with a q-dimensional objective space, we formulate a dual problem with a (q+1)-dimensional objective space. Consequently, different from an existing approach, the geometric dual problem does not depend on a fixed direction parameter, and the resulting dual image is a convex cone. We prove a one-to-one correspondence between certain faces of the primal and dual images. In addition, we show that a polyhedral approximation for one image gives rise to a polyhedral approximation for the other. Based on this, we propose a geometric dual algorithm which solves the primal and dual problems simultaneously and is free of direction-biasedness. We also modify an existing direction-free primal algorithm in such a way that it solves the dual problem as well. We test the performance of the algorithms for randomly generated problem instances by using the so-called primal error and hypervolume indicator as performance measures. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 33
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 164097235
- Full Text :
- https://doi.org/10.1137/21M1458788