[图书][B] Variational analysis and generalized differentiation II: Applications

BS Mordukhovich - 2006 - Springer
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 …

Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity

M Ahookhosh, FJ Aragón Artacho, RMT Fleming… - Advances in …, 2019 - Springer
We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear
equations. More specifically, we propose an adaptive formula for the Levenberg–Marquardt …

Error bounds in metric spaces and application to the perturbation stability of metric regularity

H Van Ngai, M Théra - SIAM Journal on Optimization, 2008 - SIAM
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 …

Inverse and implicit function theorems for H-differentiable and semismooth functions

MS Gowda - Optimization Methods and Software, 2004 - Taylor & Francis
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 …

The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditions

AF Izmailov, MV Solodov - Mathematics of Operations …, 2002 - pubsonline.informs.org
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 …

[PDF][PDF] Global linear convergence of an augmented Lagrangian algorithm to solve convex quadratic optimization problems

F Delbos, JC Gilbert - Journal of Convex Analysis, 2005 - who.rocq.inria.fr
We consider an augmented Lagrangian algorithm for minimizing a convex quadratic
function subject to linear inequality constraints. Linear optimization is an important particular …

Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods

AF Izmailov, MV Solodov - Mathematical Programming, 2003 - Springer
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 …

Second-order enhanced optimality conditions and constraint qualifications

K Bai, Y Song, J Zhang - Journal of Optimization Theory and Applications, 2023 - Springer
In this paper, we study second-order necessary optimality conditions for smooth nonlinear
programming problems. Employing the second-order variational analysis and generalized …

A class of active-set Newton methods for mixed complementarityproblems

AN Daryina, AF Izmailov, MV Solodov - SIAM Journal on Optimization, 2005 - SIAM
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 …

Critical solutions of nonlinear equations: stability issues

AF Izmailov, AS Kurennoy, MV Solodov - Mathematical Programming, 2018 - Springer
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 …