[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 …

Optimal control of the sweeping process over polyhedral controlled sets

G Colombo, R Henrion, DH Nguyen… - Journal of Differential …, 2016 - Elsevier
The paper addresses a new class of optimal control problems governed by the dissipative
and discontinuous differential inclusion of the sweeping/Moreau process while using …

A collective neurodynamic penalty approach to nonconvex distributed constrained optimization

W Jia, T Huang, S Qin - Neural Networks, 2024 - Elsevier
A nonconvex distributed optimization problem involving nonconvex objective functions and
inequality constraints within an undirected multi-agent network is considered. Each agent …

Optimal control of a nonconvex perturbed sweeping process

TH Cao, BS Mordukhovich - Journal of Differential Equations, 2019 - Elsevier
The paper concerns optimal control of discontinuous differential inclusions of the normal
cone type governed by a generalized version of the Moreau sweeping process with control …

Variational and strong variational convexity in infinite-dimensional variational analysis

PD Khanh, VVH Khoa, BS Mordukhovich… - SIAM Journal on …, 2024 - SIAM
This paper is devoted to a systematic study and characterizations of the fundamental notions
of variational and strong variational convexity for lower semicontinuous functions. While …

Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential

D Drusvyatskiy, AS Lewis - SIAM Journal on Optimization, 2013 - SIAM
Tilt Stability, Uniform Quadratic Growth, and Strong Metric Regularity of the Subdifferential Page
1 Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. OPTIM. c …

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 …

New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors

G Li, BS Mordukhovich, TS Phạm - Mathematical Programming, 2015 - Springer
In this paper we derive new fractional error bounds for polynomial systems with exponents
explicitly determined by the dimension of the underlying space and the number/degree of …