Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints

Authors:
Houyuan Jiang;Daniel Ralph
Affiliations:
CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra ACT 2601, Australia. Houyuan.Jiang@csiro.au;The Judge Institute of Management, University of Cambridge, Trumpington St., CB2 1AG, UK. danny.ralph@jims.cam.ac.uk
Venue:
Computational Optimization and Applications
Year:
2003

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Abstract

Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are proved to exhibit the local and superlinear convergence.