MultiSQP-GS: a sequential quadratic programming algorithm via gradient sampling for nonsmooth constrained multiobjective optimization

In this paper, we propose a method for solving constrained nonsmooth multiobjective optimization problems which is based on a Sequential Quadratic Programming (SQP) type approach and the Gradient Sampling (GS) technique. We consider the multiobjective problems with noncovex and nonsmooth objective and constraint functions. The problem functions are assumed to be locally Lipschitz. Such problems arise in important applications, many having (weak) Pareto solutions at points of nondifferentiability of the problem functions. In our algorithm, a penalty function is applied to regularize the constraints, GS is employed to overcome the subdifferential calculation burden and make the search direction computation effective in nonsmooth regions, and SQP is used for getting a local linearization. We prove the global convergence properties of our algorithm to the stationary points which approximate (weak) Pareto front. Furthermore, we illustrate the ability and efficiency of the proposed method via a MATLAB implementation on several tests problems and compare it with some existing algorithms.