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

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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.

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Authors and Affiliations

  1. CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra ACT, 2601, Australia

    Houyuan Jiang

  2. The Judge Institute of Management, University of Cambridge, Trumpington St, CB2 1AG, UK

    Daniel Ralph

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  1. Houyuan Jiang
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Jiang, H., Ralph, D. Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints. Computational Optimization and Applications 25, 123–150 (2003). https://doi.org/10.1023/A:1022945316191

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