An inexact multiple proximal bundle algorithm for nonsmooth nonconvex multiobjective optimization problems

For a class of nonsmooth nonconvex multiobjective problems, we develop an inexact multiple proximal bundle method. In our approach instead of scalarization, we find descent direction for every objective function separately by utilizing the inexact proximal bundle method. Then we attempt to find a common descent direction for all objective functions. We study the effect of the inexactness of the objective and subgradient values on the new proposed method and obtain the reasonable convergence properties. We further consider a class of difficult nonsmooth nonconvex problems, made even more difficult by inserting the inexactness in the available information. At the end, to demonstrate the efficiency of the proposed algorithm, some encouraging numerical experiments are provided.