Gradient Sampling Methods with Inexact Subproblem Solutions and Gradient Aggregation

Gradient sampling (GS) methods for the minimization of objective functions that may be nonconvex and/or nonsmooth are proposed, analyzed, and tested. One most computationally expensive components contemporary GS is need to solve a convex quadratic subproblem in each iteration. By contrast, proposed this paper allow use inexact solutions these subproblems, which, as proved paper, can incorporated without loss theoretical convergence guarantees. Numerical experiments show that, by exploiting solutions, one consistently reduce computational effort required method. Additionally, strategy aggregating gradient information after solved (potentially inexactly) has been exploited bundle optimization. It aggregation scheme introduced incorporating approach also