Abstract
Using a directional form of constraint qualification weaker than Robinson's, we derive an implicit function theorem for inclusions and use it for first- and second-order sensitivity analyses of the value function in perturbed constrained optimization. We obtain Hölder and Lipschitz properties and, under a no-gap condition, first-order expansions for exact and approximate solutions. As an application, differentiability properties of metric projections in Hilbert spaces are obtained, using a condition generalizing polyhedricity. We also present in the appendix a short proof of a generalization of the convex duality theorem in Banach spaces.
Original language | English |
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Pages (from-to) | 1151-1171 |
Number of pages | 21 |
Journal | SIAM Journal on Control and Optimization |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - Jul 1996 |
Keywords
- Approximate solutions
- Convex duality
- Directional constraint qualification
- Marginal function
- Regularity and implicit function theorems
- Sensitivity analysis