A nonmonotone line search method for solving constrained multiobjective optimization problems

In this paper, we propose a globally convergent Sequential Quadratic Programming (SQP) method for solving constrained multiobjective optimization problems (MOPs) with inequality constraints. At each iteration, a feasible descent direction is computed by solving an auxiliary quadratic programming subproblem constructed from linear approximations of the objective and constraint functions. Constraint violations are addressed using a nonsmooth exact penalty function. Moreover, the algorithm incorporates a nonmonotone max-type line-search strategy, which improves practical performance by allowing temporary increases in the penalty function value and thereby promoting more effective exploration of the search space. Under mild regularity assumptions, we prove that the sequence generated by the method converges to a weakly or strongly critical point. Numerical experiments on standard benchmark problems demonstrate the effectiveness and robustness of the proposed approach, both in terms of computational performance criteria and the quality of the approximated Pareto front.

کلیدواژه ها:

SQP method ، Nonmonotone line search ، Penalty method ، Mangasarian–Fromovitz constraint qualification ، Critical point