Normal maps inducted by linear transformations
Mathematics of Operations Research
On branching numbers of normal manifolds
Nonlinear Analysis: Theory, Methods & Applications
Implicit multifunction theorems for the sensitivity analysis of variational conditions
Mathematical Programming: Series A and B
Lipschitzian Multifunctions and a Lipschitzian Inverse Mapping Theorem
Mathematics of Operations Research
Solution Sensitivity from General Principles
SIAM Journal on Control and Optimization
Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
SIAM Journal on Optimization
Ample Parameterization of Variational Inclusions
SIAM Journal on Optimization
A Linearization Method for Nondegenerate Variational Conditions
Journal of Global Optimization
Mathematics of Operations Research
Generalized Poincaré-Hopf Theorem for Compact Nonsmooth Regions
Mathematics of Operations Research
Variational Stability and Marginal Functions via Generalized Differentiation
Mathematics of Operations Research
Local Duality of Nonlinear Semidefinite Programming
Mathematics of Operations Research
Variational Conditions Under the Constant Rank Constraint Qualification
Mathematics of Operations Research
Generic Optimality Conditions for Semialgebraic Convex Programs
Mathematics of Operations Research
Hi-index | 0.00 |
This paper studies the sensitivity analysis of variational conditions defined over perturbed systems of finitely many nonlinear inequalities or equations, subject to additional fixed polyhedral constraints. If the system of constraints obeys a certain property called nondegeneracy, we show how to construct a local diffeomorphism of the feasible set to its tangent cone. Moreover, this diffeomorphism varies smoothly as the perturbation parameter changes.The original variational condition is then locally equivalent to a variational inequality defined over this (polyhedral convex) tangent cone. This extends stability results already known for variational inequalities over polyhedral convex sets to a substantially more general case. We also show that existence, local uniqueness, and Lipschitz continuity, as well as B-differentiability of the solution, can all be predicted from a single affine variational inequality that is easily computable in terms of the data of the unperturbed problem at the point in question.