On the computation of relaxed pessimistic solutions to MPECs

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this paper, we propose a new numerical method to compute approximate and the so-called relaxed pessimistic solutions to mathematical programs with equilibrium constraints (MPECs), where the solution map arising in the equilibrium constraints is not single-valued. This method combines two types of existing codes, a code for derivative-free optimization under box constraints, BFO or BOBYQA, and a method for solving special parametric MPECs from the interactive system UFO. We report on numerical performance in several small-dimensional test problems.