315. Relying on first-order methods to deal with utility functions-based scalarization in multi-objective optimization
Invited abstract in session FB-2: First-order methods for multi-level and multi-objective optimization, stream Advances in first-order optimization.
Friday, 10:05 - 11:20Room: M:O
Authors (first author is the speaker)
| 1. | Lorenzo Lampariello
|
| Roma Tre University | |
| 2. | Simone Sagratella
|
| Ingegneria informatica automatica e gestionale A. Ruberti, La Sapienza Università di Roma | |
| 3. | Valerio Giuseppe Sasso
|
| Dipartimento di ingegneria Informatica, Automatica e Gestionale, Sapienza Università di Roma | |
| 4. | Vladimir Shikhman
|
| Chemnitz University of Technology |
Abstract
We study a general scalarization approach via utility functions in multi-objective optimization. It consists of maximizing utility that is obtained from the objectives’ bargaining with regard to a disagreement reference point.
We propose a gradient-based numerical scheme to solve utility-dependent single-objective optimization problems. Here, the main difficulty comes from the necessity to address constraints which are associated with a disagreement reference point. Our crucial observation is that the explicit treatment of these additional constraints may be avoided. This is the case if the Slater condition is satisfied and the utility function under consideration has the so-called barrier property. Under these assumptions, we prove the convergence of our scheme to Pareto optimal points.
Preliminary numerical experiments on real-world financial datasets in a portfolio selection context confirm the efficiency of our approach.
Keywords
- SS - Advances in Nonlinear Optimization and Applications
- SS - Multiobjective Optimization
- Analysis and engineering of optimization algorithms
Status: accepted
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