Article ID: | iaor20032538 |
Country: | Germany |
Volume: | 93 |
Issue: | 2 |
Start Page Number: | 265 |
End Page Number: | 279 |
Publication Date: | Jan 2002 |
Journal: | Mathematical Programming |
Authors: | Ralph D., Hu X. |
Using standard nonlinear programming (NLP) theory, we establish formulas for first and second order directional derivatives of optimal value functions of parametric mathematical programs with complementarity constraints (MPCCs). The main point is that under a linear independence condition on the active constraint gradients, optimal value sensitivity of MPCCs is essentially the same as for nonlinear programs, in spite of the combinatorial nature of the MPCC feasible set. Unlike NLP however, second order directional derivatives of the MPCC optimal value function show combinatorial structure.