Constrained Multi-Objective Optimization

ICLR 2025 Conference Submission12704 Authors

Keywords: constrained multi-objective optimization, multi-gradient descent algorithms

Abstract: There is more and more attention on constrained multi-objective optimization (CMOO) problems, however, most of them are based on gradient-free methods. This paper proposes a constraint gradient-based algorithm for multi-objective optimization (MOO) problems based on multi-gradient descent algorithms. We first establish a framework for the CMOO problem. Then, we provide a Moreau envelope-based Lagrange Multiplier (MLM-CMOO) algorithm to solve the formulated CMOO problem, and the convergence analysis shows that the proposed algorithm convergence to Pareto stationary solutions with a rate of $\mathcal{O}(\frac{1}{\sqrt{T}})$. Finally, the MLM-CMOO algorithm is tested on several CMOO problems and has shown superior results compared to some chosen state-of-the-art designs.

Primary Area: optimization

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Submission Number: 12704