Research On The Smoothing Algorithm And The SQP Method For Mathematical Programs With Equilibrium Constraints

In recent years, mathematical programs with equilibrium constraints have become afocus in operational research. It stem from game theory and is widely applied in economicanalysis natural science and engineering computation. However, finding the numericalmethods to it. becomes very difficult since the complexity of its feasible field. Up to now,only a few algorithms have been presented for solving it.The main results obtained in the paper as follows:Using the idea of F.Facchinei, H.Y.Jiang and L.Qi[26], a smoothing continuationalgorithm for solving mathematical programs with equilibrium constraints is presentedunder the monotone and strong second-order sufficient condition. The smooth nonliearprogram subproblems of the algorithm is proved to be always feasible. Under the strictcomplementarity condition, it is proved that the stationary point sequence convergenceto B stationary point of mathematical programs with equilibrium constraints.Also, a modified quadratic programing subproblem which is always feasible is con-structed by introducing a artificial variableξ, and then a SQP method for mathematicalprograms with equilibrium constraints is presented. Under the strict complementaritycondition at the accumalation points of the sequence of iterations, the global convergenceof the algorithm is proved.