A note on sensitivity of value functions of mathematical programs with complementarity constraints |
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Authors: | Xinmin Hu Daniel Ralph |
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Institution: | (1) Department of Mathematics and Statistics, The University of Melbourne, AU;(2) Judge Institute of Management, The University of Cambridge, GB |
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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.
Received: October 31, 2000 / Accepted: March 8, 2002?Published online June 25, 2002 |
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