Lipschitzian stability of constraint systems and generalized equations
Nonlinear Analysis: Theory, Methods & Applications
Stablity of Set-Valued Mappings In Infinite Dimensions: Point Criteria and Applications
SIAM Journal on Control and Optimization
Coderivatives of multivalued mappings, locally compact cones and metric regularity
Nonlinear Analysis: Theory, Methods & Applications
Tilt Stability of a Local Minimum
SIAM Journal on Optimization
Stability of Locally Optimal Solutions
SIAM Journal on Optimization
Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
SIAM Journal on Optimization
On Second-Order Subdifferentials and Their Applications
SIAM Journal on Optimization
Variational Stability and Marginal Functions via Generalized Differentiation
Mathematics of Operations Research
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The paper mostly concerns applications of the generalized differentiation theory in variational analysis to Lipschitzian stability and metric regularity of variational systems in infinite-dimensional spaces. The main tools of our analysis involve coderivatives of set-valued mappings that turn out to be proper extensions of the adjoint derivative operator to nonsmooth and set-valued mappings. The involved coderivatives allow us to give complete dual characterizations of certain fundamental properties in variational analysis and optimization related to Lipschitzian stability and metric regularity. Based on these characterizations and extended coderivative calculus, we obtain efficient conditions for Lipschitzian stability of variational systems governed by parametric generalized equations and their specifications.