A note on sensitivity of value functions of mathematical programs with complementarity constraints

A note on sensitivity of value functions of mathematical programs with complementarity constraints

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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: ,
Abstract:

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.

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