## Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints (2005)

Venue: | Industrial Engineering & Management Sciences, Northwestern University |

Citations: | 15 - 0 self |

### BibTeX

@TECHREPORT{Liu05generalizedstationary,

author = {Xinwei Liu and Jie Sun},

title = {Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints},

institution = {Industrial Engineering & Management Sciences, Northwestern University},

year = {2005}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. 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. Key words: Global convergence, interior-point methods, mathematical programming with equilibrium constraints, stationary point