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: | Dempe S. |
Keywords: | programming: parametric |
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.