Necessary Optimality Conditions for Two-Stage Stochastic Programs with Equilibrium Constraints
SIAM Journal on Optimization
Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
SIAM Journal on Optimization
Calmness of efficient solution maps in parametric vector optimization
Journal of Global Optimization
Stability of Error Bounds for Convex Constraint Systems in Banach Spaces
SIAM Journal on Optimization
Parametric Nonlinear Programming Problems under the Relaxed Constant Rank Condition
SIAM Journal on Optimization
SIAM Journal on Optimization
Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions
Journal of Global Optimization
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The paper is devoted to the analysis of the calmness property for constraint set mappings. After some general characterizations, specific results are obtained for various types of constraints, e.g., one single nonsmooth inequality, differentiable constraints modeled by polyhedral sets, finitely and infinitely many differentiable inequalities. The obtained conditions enable the detection of calmness in a number of situations, where the standard criteria (via polyhedrality or the Aubin property) do not work. Their application in the framework of generalized differential calculus is explained and illustrated by examples associated with optimization and stability issues in connection with nonlinear complementarity problems or continuity of the value-at-risk.