2377. Bilevel Gradient Algorithms for Optimization over the Pareto Set
Invited abstract in session TD-51: Advances in nonlinear multiobjective optimization, stream Multiobjective and vector optimization.
Tuesday, 14:30-16:00Room: Parkinson B22
Authors (first author is the speaker)
| 1. | Yumi Kitazume
|
| Science and Engineering, Seikei University | |
| 2. | Takayuki Okuno
|
| Seikei University |
Abstract
A multi-objective optimization problem is a classical optimization problem that seeks to optimize multiple objective functions simultaneously and has numerous practical applications. In practice, the primary goal of solving such problems is to identify the so-called Pareto set and then determine an optimal point according to specific criteria by decision-makers.
In this research, we aim to optimize a scalar function over the Pareto set. To address this problem, we propose a new approach based on three steps. First, we formulate the problem as a bilevel optimization problem, where the lower-level problem is a multi-objective optimization problem. Second, we transform the lower-level problem into a single-objective (possibly nonsmooth) problem using a scalarization method for multi-objective optimization. Third, we construct a certain unconstrained optimization problem by approximating the lower-level solution using a finite number of iterations of a gradient algorithm combined with a smoothing technique, and then apply a gradient algorithm to the obtained problem.
We establish global asymptotic convergence results under mild assumptions and further demonstrate the efficiency of the proposed approach through numerical experiments.
Keywords
- Programming, Multi-Objective
- Programming, Nonlinear
Status: accepted
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