Directional differentiability of optimal solutions under Slater’s condition

Directional differentiability of optimal solutions under Slater’s condition

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Article ID: iaor19941888
Country: Netherlands
Volume: 59
Issue: 1
Start Page Number: 49
End Page Number: 69
Publication Date: Mar 1993
Journal: Mathematical Programming (Series A)
Authors:
Keywords: programming: parametric
Abstract:

For convex parametric optimization problems it is shown that the optimal solution is directionally differentiable provided that a strong second-order sufficient optimality condition and Slater’s condition are satisfied for the unperturbed problem. This directional derivative is equal to the optimal solution of a certain quadratic programming problem. For the construction of this quadratic problem, a preliminary choice of a ‘suitable’ KKT-multiplier is necessary, which under additional assumptions may be taken as a vertex of the set of KKT-multipliers of the unperturbed problem. In the last part of this paper, the contingent derivative of the optimal solution is investigated.

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