Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints
Year: 2010
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2010.33.6
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 3 : pp. 367–386
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Mathematical programs with complementarity constraints nonlinear complementarity constraints aggregation technique S-stationary point global convergence super-linear convergence.