A Decomposition Method with Redistributed Subroutine for Constrained Nonconvex Optimization

Abstract

A class of constrained nonsmooth nonconvex optimization problems, that is, piecewise $C^2$ objectives with smooth inequality constraints are discussed in this paper. Based on the $𝒱𝒰$-theory, a superlinear convergent $𝒱𝒰$-algorithm, which uses a nonconvex redistributed proximal bundle subroutine, is designed to solve these optimization problems. An illustrative example is given to show how this convergent method works on a Second-Order Cone programming problem.