Variational analysis has been recognized as a fruitful area in mathematics that on the one
hand deals with the study of optimization and equilibrium problems and on the other hand …

We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear
equations. More specifically, we propose an adaptive formula for the Levenberg–Marquardt …

This paper was motivated by the need to establish some new characterizations of the metric
regularity of set-valued mappings. Through these new characterizations it was possible to …

In this article, we prove inverse and implicit function theorems for H-differentiable functions,
thereby giving a unified treatment of such theorems for C 1-functions, PC 1-functions, and for …

We study local structure of a nonlinear mapping near points where standard regularity
and/or smoothness assumptions need not be satisfied. We introduce a new concept of 2 …

We consider an augmented Lagrangian algorithm for minimizing a convex quadratic
function subject to linear inequality constraints. Linear optimization is an important particular …

We consider optimality systems of Karush-Kuhn-Tucker (KKT) type, which arise, for example,
as primal-dual conditions characterizing solutions of optimization problems or variational …

In this paper, we study second-order necessary optimality conditions for smooth nonlinear
programming problems. Employing the second-order variational analysis and generalized …

Based on the identification of indices active at a solution of the mixed complementarity
problem (MCP), we propose a class of Newton methods for which local superlinear …

It is known that when the set of Lagrange multipliers associated with a stationary point of a
constrained optimization problem is not a singleton, this set may contain so-called critical …