An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Benson's algorithm for nonconvex multiobjective problems via nonsmooth Wolfe duality

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...

An inexact modified subgradient algorithm for nonconvex optimization

We propose and analyze an inexact version of the modified subgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the IMSG algorithm. Inexact minimization may a...

A proximal bundle method for nonsmooth nonconvex functions with inexact information

For a class of nonconvex nonsmooth functions, we consider the problem of computing an approximate critical point, in the case when only inexact information about the function and subgradient values is available. We assume that the errors in function and subgradient evaluations are merely bounded, and in principle need not vanish in the limit. We examine the redistributed proximal bundle approac...

A Proximal Bundle Method for Nonconvex Functions with Inexact Oracles

For a class of nonconvex nonsmooth functions, we consider the problem of computing an approximate critical point, in the case of inexact oracles. The latter means that only an inexact function value and an inexact subgradient are available, at any given point. We assume that the errors in function and subgradient evaluations are merely bounded, and in principle need not vanish in the limit. We ...