[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 …

Subdifferentials of nonconvex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data

BS Mordukhovich, TTA Nghia - SIAM Journal on Optimization, 2013 - SIAM
The paper is devoted to the subdifferential study and applications of the supremum of
uniformly Lipschitzian functions over arbitrary index sets with no topology. Based on …

Variational geometric approach to generalized differential and conjugate calculi in convex analysis

BS Mordukhovich, NM Nam, RB Rector… - Set-Valued and Variational …, 2017 - Springer
This paper develops a geometric approach of variational analysis for the case of convex
objects considered in locally convex topological spaces and also in Banach space settings …

Stationarity and regularity of infinite collections of sets

AY Kruger, MA López - Journal of Optimization Theory and Applications, 2012 - Springer
This article investigates extremality, stationarity, and regularity properties of infinite
collections of sets in Banach spaces. Our approach strongly relies on the machinery …

New extremal principles with applications to stochastic and semi-infinite programming

BS Mordukhovich, P Pérez-Aros - Mathematical Programming, 2021 - Springer
This paper develops new extremal principles of variational analysis that are motivated by
applications to constrained problems of stochastic programming and semi-infinite …

Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

AY Kruger, MA López - Journal of Optimization Theory and Applications, 2012 - Springer
This article continues the investigation of stationarity and regularity properties of infinite
collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl …

Subdifferential formulae for the supremum of an arbitrary family of functions

P Pérez-Aros - SIAM Journal on Optimization, 2019 - SIAM
This work provides calculus rules for the Fréchet and Mordukhovich subdifferentials of the
pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start …

Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets

NC Hung, TD Chuong, NLH Anh - Journal of Optimization Theory and …, 2024 - Springer
In this paper, we study a robust optimization problem whose constraints include nonsmooth
and nonconvex functions and the intersection of closed sets. Using advanced variational …

Lagrange multiplier characterizations of constrained best approximation with infinite constraints

H Bakhtiari, H Mohebi - Journal of Optimization Theory and Applications, 2021 - Springer
In this paper, we first employ the subdifferential closedness condition and Guignard's
constraint qualification to present “dual cone characterizations” of the constraint set Ω with …

Exact separation theorem for disjoint closed sets in Hilbert spaces

B Zhang, F Yu - Optimization Letters, 2024 - Springer
Using techniques of variational analysis and in terms of proximal normal cones, we establish
exact separation results for finitely many disjoint closed sets in Hilbert spaces without …