An aggregate subgradient method for nonsmooth and nonconvex minimization

This paper presents a readily implementable algorithm for minimizing a locally Lipschitz continuous function that is not necessarily convex or differentiable. This extension of the aggregate subgradient method differs from one developed by the author in the treatment of nonconvexity. Subgradient aggregation allows the user to control the number of constraints in search direction finding subproblems and, thus, trade-off subproblem solution effort for rate of convergence. All accumulation points of the algorithm are stationary. Moreover, the algorithm converges when the objective function happens to be convex.