Boris S. Mordukhovich Page 1 Springer Monographs in Mathematics Boris S. Mordukhovich
Variational Analysis and Applications Page 2 Springer Monographs in Mathematics Editors-in-Chief …

The proximal gradient algorithm for minimizing the sum of a smooth and nonsmooth convex
function often converges linearly even without strong convexity. One common reason is that …

Optimization algorithms can see their local convergence rates deteriorate when the Hessian
at the optimum is singular. These singularities are inescapable when the optima are non …

In this paper, we study the efficiency of a Restarted SubGradient (RSG) method that
periodically restarts the standard subgradient method (SG). We show that, when applied to a …

We present a framework for analyzing convergence and local rates of convergence of a
class of descent algorithms, assuming the objective function is weakly convex. The …

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a
broad class of nonsmooth composite convex optimization problems without strong convexity …

In this short survey, I revisit the role of the proximal point method in large scale optimization. I
focus on three recent examples: a proximally guided subgradient method for weakly convex …

This paper proposes and justifies two globally convergent Newton-type methods to solve
unconstrained and constrained problems of nonsmooth optimization by using tools of …

We consider optimization algorithms that successively minimize simple Taylor-like models of
the objective function. Methods of Gauss–Newton type for minimizing the composition of a …

The paper is devoted to the study, characterizations, and applications of variational
convexity of functions, the property that has been recently introduced by Rockafellar together …