A proximal bundle method-based algorithm with penalty strategy and inexact oracles for constrained nonsmooth nonconvex optimization

Abstract

In this paper, we consider a class of nonconvex nonsmooth constrained problems with inexact data. To deal with the constraints, the penalty strategy is adopted during the process to transfer the primal problem into an unconstrained problem. For inexact data, we add quadratic term with variable coefficient to each term in the unconstrained problem to keep the corresponding linearization errors nonnegative. For the modified unconstrained problem, we utilize the disaggregate technique and design corresponding cutting planes for each function. Meanwhile, the sum of the corresponding cutting planes is regarded as the cutting plane for the modified unconstrained problem and proximal bundle method is adopted to deal with the model. The preliminary numerical results show our algorithm is effective and attractive.