A Multi-objective Sequential Quadratic Programming Algorithm Based on Low-order Smooth Penalty Function

Abstract: In this paper,we propose a Multi-Objective Sequential Quadratic Programming (MOSQP) algorithm for constrained multi-objective optimization problems,basd on a low-order smooth penalty function as the merit function for line search. The algorithm constructs single-objective optimization subproblems based on each objective function, solves quadratic programming (QP) subproblems to obtain descent directions for expanding the iterative point set within the feasible region, and filters non-dominated points after expansion. A new QP problem is then formulated using information from all objective functions to derive descent directions. The Armijo step size rule is employed for line search, combined with Powell's correction formula (1978) for B iteration updates. If QP subproblems is infesible, the negative gradient of the merit function is adopted as the search direction. The algorithm is proven to converge to an approximate Pareto front for constrained multi-objective optimization. Finally, numerical experiments are performed for specific multi-objective optimization problems.