A generalized project metric algorithm for mathematical programs with equilibrium constraints

Minglei Fang ^[1] ; Zhibin Zhu ^[2]
1. [1] Anhui University of Science and Technology
  
  Anhui University of Science and Technology
  
  China
2. [2] Guilin University of Electronic Technology
  
  Guilin University of Electronic Technology
  
  China
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 288, Nº 1 (November 2015), 2015, págs. 99-115
Idioma: inglés
DOI: 10.1016/j.cam.2015.04.007
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Resumen
- This paper discusses a kind of mathematical programs with equilibrium constraints (MPEC for short). By using a complementarity function and a kind of disturbed technique, the original (MPEC) problem is transformed into a nonlinear equality and inequality constrained optimization problem. Then, we combine a generalized gradient projection matrix with penalty function technique to given a generalized project metric algorithm with arbitrary initial point for the (MPEC) problems. In order to avoid Mataros effect, a high-order revised direction is obtained by an explicit formula. Under some relative weaker conditions, the proposed method is proved to possess global convergence and superlinear convergence.