[图书][B] Variational analysis and applications

BS Mordukhovich - 2018 - Springer
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 …

Error bounds, quadratic growth, and linear convergence of proximal methods

D Drusvyatskiy, AS Lewis - Mathematics of Operations …, 2018 - pubsonline.informs.org
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 …

Second-order growth, tilt stability, and metric regularity of the subdifferential

D Drusvyatskiy, BS Mordukhovich… - arXiv preprint arXiv …, 2013 - arxiv.org
This paper sheds new light on several interrelated topics of second-order variational
analysis, both in finite and infinite-dimensional settings. We establish new relationships …

Globally convergent coderivative-based generalized Newton methods in nonsmooth optimization

PD Khanh, BS Mordukhovich, VT Phat… - Mathematical …, 2024 - Springer
This paper proposes and justifies two globally convergent Newton-type methods to solve
unconstrained and constrained problems of nonsmooth optimization by using tools of …

Variational convexity of functions and variational sufficiency in optimization

PD Khanh, BS Mordukhovich, VT Phat - SIAM Journal on Optimization, 2023 - SIAM
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 …

Complete characterizations of tilt stability in nonlinear programming under weakest qualification conditions

H Gfrerer, BS Mordukhovich - SIAM Journal on Optimization, 2015 - SIAM
This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear
programs with equality and inequality constraints in finite dimensions described by twice …

A generalized Newton method for subgradient systems

P Duy Khanh, B Mordukhovich… - … of Operations Research, 2023 - pubsonline.informs.org
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 …

[HTML][HTML] On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives

H Gfrerer, JV Outrata - Journal of Mathematical Analysis and Applications, 2022 - Elsevier
The paper deals with a comprehensive theory of mappings, whose local behavior can be
described by means of linear subspaces, contained in the graphs of two (primal and dual) …

Full Lipschitzian and Holderian stability in optimization with applications to mathematical programming and optimal control

BS Mordukhovich, TTA Nghia - SIAM Journal on Optimization, 2014 - SIAM
The paper concerns a systematic study of full stability in general optimization models
including its conventional Lipschitzian version as well as the new Hölderian one. We …

Full stability in finite-dimensional optimization

BS Mordukhovich, TTA Nghia… - Mathematics of …, 2015 - pubsonline.informs.org
The paper is devoted to full stability of optimal solutions in general settings of finite-
dimensional optimization with applications to particular models of constrained optimization …