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

Houyuan Jiang (Houyuan.Jiangcsiro.au)
Daniel Ralph (danny.ralphjims.cam.ac.uk)

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.

Keywords: Mathematical programs with equilibrium constraints, MPEC, MPCC, complementarity problem, complementarity constraints, piecewise sequential quadratic programming, quasi-Newton method, superlinear convergence.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Complementarity and Variational Inequalities

Citation: Unpublished. Judge Institute of Management, Cambridge University, Trumpington St, Cambridge, CB2 1AG, UK, 2002.

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Entry Submitted: 09/02/2002
Entry Accepted: 09/02/2002
Entry Last Modified: 09/02/2002

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