[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 …
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 …
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 …
objects considered in locally convex topological spaces and also in Banach space settings …
Stationarity and regularity of infinite collections of sets
This article investigates extremality, stationarity, and regularity properties of infinite
collections of sets in Banach spaces. Our approach strongly relies on the machinery …
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 …
applications to constrained problems of stochastic programming and semi-infinite …
Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization
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 …
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 …
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
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 …
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 …
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 …
exact separation results for finitely many disjoint closed sets in Hilbert spaces without …