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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: October 31, 2000 / Accepted: March 8, 2002¶Published online June 25, 2002
Rights and permissions
About this article
Cite this article
Hu, X., Ralph, D. A note on sensitivity of value functions of mathematical programs with complementarity constraints. Math. Program. 93, 265–279 (2002). https://doi.org/10.1007/s10107-002-0301-6
Issue Date:
DOI: https://doi.org/10.1007/s10107-002-0301-6