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An exact penalty method with nonmonotone line search and rapid infeasibility detection for constrained multiobjective optimization: Application in supervised machine learning
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DOI：10.1016/j.cor.2025.107351.png)
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Abstract
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In this paper, we propose a nonmonotone line search method within the Sequential Quadratic Programming (SQP) framework for solving constrained Multiobjective Problems (MOPs), using an exact penalty function. Our approach improves infeasibility detection and simplifies penalty parameter updates. The algorithm solves up to two inequality-constrained subproblems per iteration and uses trust regions for penalty updates, combining the benefits of trust regions and line search methods. A nonmonotone line search allows temporary increases in the penalty function, helping the algorithm explore the search space more effectively, especially in nonconvex problems. It provides flexibility, enabling the algorithm to find better solutions that meet constraints and move closer to optimality, even when regions near feasibility still violate some constraints. Our method targets (weakly) efficient points in feasible MOPs and stationary points for constraint violations in infeasible cases. We prove the algorithm’s global convergence and validate its effectiveness with several numerical tests. We analyze the performance of our algorithm using various metrics. Finally, we apply the algorithm to a challenging problem in supervised machine learning, aiming to minimize data misclassification, and then to a financial management problem involving return prediction using real market data. Initially developed for multiobjective problems, our approach also improves some methods designed for single-objective problems.
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