Second-order sufficient conditions for local optimality have long been central to designing
solution algorithms and justifying claims about their convergence. Here a far-reaching …

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

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 …

Strong variational sufficiency is a newly proposed property, which turns out to be of great
use in the convergence analysis of multiplier methods. However, what this property implies …

In this paper, we readdress the classical topic of second-order sufficient optimality conditions
for optimization problems with nonsmooth structure. Based on the so-called second …

This paper proposes and develops a new Newton-type algorithm to solve subdifferential
inclusions defined by subgradients of extended real-valued prox-regular functions. The …

The paper is devoted to a comprehensive study of composite models in variational analysis
and optimization the importance of which for numerous theoretical, algorithmic, and applied …

In this paper, we propose second-order sufficient optimality conditions for a very general
nonconvex constrained optimization problem, which covers many prominent mathematical …

The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued
functions, with an emphasis on functions satisfying a certain composite representation. This …

This paper aims at developing two versions of the generalized Newton method to compute
local minimizers for nonsmooth problems of unconstrained and constrained optimization that …