A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems

We propose a class of infeasible proximal bundle methods for solving nonsmooth nonconvex multi-objective optimization problems. The proposed algorithms have no requirements on the feasibility of the initial points. In the algorithms, the multi-objective functions are handled directly without any scalarization procedure. To speed up the convergence of the infeasible algorithm, an acceleration technique, i.e., the penalty skill, is applied into the algorithm. The strategies are introduced to adjust the proximal parameters and penalty parameters. Under some wild assumptions, the sequence generated by infeasible proximal bundle methods converges to the globally Pareto solution of multi-objective optimization problems. Numerical results shows the good performance of the proposed algorithms.