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B. Mordukhovich, B. Wang (2003)
Calculus of sequential normal compactness in variational analysisJournal of Mathematical Analysis and Applications, 282
H. Gfrerer (2014)
Optimality Conditions for Disjunctive Programs Based on Generalized Differentiation with Application to Mathematical Programs with Equilibrium ConstraintsSIAM J. Optim., 24
J. Penot (2014)
Directionally limiting subdifferentials and second-order optimality conditionsOptimization Letters, 8
B. Mordukhovich (2006)
Variational Analysis and Generalized Differentiation II: Applications
B. Mordukhovich, B. Wang (2004)
Restrictive metric regularity and generalized differential calculus in Banach spacesInt. J. Math. Math. Sci., 2004
Karolin Papst (2016)
Techniques Of Variational Analysis
R. Rockafellar (1988)
First- and second-order epi-differentiability in nonlinear programmingTransactions of the American Mathematical Society, 307
I. Ginchev, B. Mordukhovich (2012)
Directional subdifferentials and optimality conditionsPositivity, 16
H. Gfrerer, D. Klatte (2016)
Lipschitz and Hölder stability of optimization problems and generalized equationsMathematical Programming, 158
B. Mordukhovich, Y. Shao (1996)
Nonsmooth sequential analysis in Asplund spacesTransactions of the American Mathematical Society, 348
C. Chou, Xinbao Li, K. Ng, Shuzhong Shi (1996)
Optimality Conditions for Lower Semi-continuous FunctionsJournal of Mathematical Analysis and Applications, 202
H Gfrerer (2013)
On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programsSet-Valued Var. Anal., 21
R. Chaney (1985)
On second derivatives for nonsmooth functionsNonlinear Analysis-theory Methods & Applications, 9
B. Mordukhovich, Y. Shao (1995)
On Nonconvex Subdifferential Calculus in Banach Spaces
R. Chaney (1987)
Second-order necessary conditions in constrained semismooth optimizationSiam Journal on Control and Optimization, 25
M. Fabian, B. Mordukhovich (2003)
Sequential normal compactness versus topological normal compactness in variational analysisNonlinear Analysis-theory Methods & Applications, 54
R. Chaney (1987)
Second-order directional derivatives for nonsmooth functionsJournal of Mathematical Analysis and Applications, 128
B. Wang, Xinmin Yang (2016)
Weak Differentiability with Applications to Variational AnalysisSet-Valued and Variational Analysis, 24
(2003)
Finite-dimensional Variational Inequalities and Complementary Problems, vols
B. Mordukhovich, N. Nam (2005)
Variational Stability and Marginal Functions via Generalized DifferentiationMath. Oper. Res., 30
R. Phelps (1989)
Convex Functions, Monotone Operators and Differentiability
L. Huang, K. Ng (1994)
Second-order necessary and sufficient conditions in nonsmooth optimizationMathematical Programming, 66
J. Penot (2011)
The directional subdifferential of the difference of two convex functionsJournal of Global Optimization, 49
(1996)
On some relations between Chaney’s generalized second order directional derivative and that of Ben-Tal and Zowe
I Ginchev, BS Mordukhovich (2011)
On directionally dependent subdifferentialsC. R. Bulg. Acad. Sci., 64
BS Mordukhovich (2006)
Variational Analysis and Generalized Differentiation I: Basic Theory
H. Gfrerer (2012)
JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics On Directional Metric Regularity, Subregularity and Optimality Conditions for Nonsmooth Mathematical Programs
M. Fabian (1989)
Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss, 030
I. Ginchev, B. Mordukhovich (2010)
On directionally dependent subdifferentialsComptes Rendus De L Academie Bulgare Des Sciences, 64
F. Clarke (1983)
Optimization And Nonsmooth Analysis
Bastian Goldlücke (2014)
Variational Analysis
B. Mordukhovich, Y. Shao (1996)
Extremal characterizations of asplund spaces, 124
W Rudin (1991)
Functional Analysis
A. Ioffe (1990)
Proximal Analysis and Approximate SubdifferentialsJournal of The London Mathematical Society-second Series
In this work we study the directional versions of Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions in the framework of general Banach spaces. We establish some characterizations and basic properties of these constructions, and then develop calculus including sum rules and chain rules involving smooth functions. As an application, we also explore the upper estimates of the directional Mordukhovich subdifferentials and singular subdifferentials of marginal functions.
Positivity – Springer Journals
Published: Apr 27, 2016
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