Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
نویسندگان
چکیده
Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). Under certain general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point.
منابع مشابه
Generalized Stationary Points and an Interior Point Method for MPEC
Mathematical program with equilibrium constraints (MPEC) has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC. A primal-dual interior point method is then proposed, which solves a sequence of relaxe...
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ورودعنوان ژورنال:
- Math. Program.
دوره 101 شماره
صفحات -
تاریخ انتشار 2004