Nonsmooth multiobjective programming with quasi-Newton methods

•A nonsmooth quasi-Newton algorithm is proposed for solving nonsmooth multiple objective programming.•A tractable subproblem is solved to obtain the descent direction.•The global and local convergence results for the new algorithm are presented under reasonable assumptions.•The efficiency of the new algorithm is shown by a numerical example.

This paper proposes a new algorithm to solve nonsmooth multiobjective programming. The algorithm is a descent direction method to obtain the critical point (a necessary condition for Pareto optimality). We analyze both global and local convergence results under some assumptions. Numerical tests are also given.