@Article{NMTMA-3-3, author = {}, title = {Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {3}, pages = {367--386}, abstract = {
Mathematical programs with complementarity constraints (MPCC) is an important subclass of MPEC. It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem. In this paper, we propose a new smoothing method for MPCC by using the aggregation technique. A new SQP algorithm for solving the MPCC problem is presented. At each iteration, the master direction is computed by solving a quadratic program, and the revised direction for avoiding the Maratos effect is generated by an explicit formula. As the non-degeneracy condition holds and the smoothing parameter tends to zero, the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem, its convergence rate is superlinear. Some preliminary numerical results are reported.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.33.6}, url = {https://global-sci.com/article/90731/superlinear-convergence-of-a-smooth-approximation-method-for-mathematical-programs-with-nonlinear-complementarity-constraints} }