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Formulating and Solving Nonlinear Programs as Mixed Complementarity Problems

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Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 481))

Abstract

We consider a primal-dual approach to solve nonlinear programming problems within the AMPL modeling language, via a mixed complementarity formulation. The modeling language supplies the first order and second order derivative information of the Lagrangian function of the nonlinear problem using automatic differentiation. The PATH solver finds the solution of the first order conditions which are generated automatically from this derivative information. In addition, the link incorporates the objective function into a new merit function for the PATH solver to improve the capability of the complementarity algorithm for finding optimal solutions of the nonlinear program. We test the new solver on various test suites from the literature and compare with other available nonlinear programming solvers.

This research was partially supported by National Science Foundation Grant CCR-9619765 and Air Force Office of Scientific Research Grant F49620-98-1- 0417

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Author information

Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, Wisconsin, 53706

    Michael C. Ferris & Krung Sinapiromsaran

Authors
  1. Michael C. Ferris
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  2. Krung Sinapiromsaran
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Namur, Rue de Bruxelles 61, 5000, Namur, Belgium

    Van Hien Nguyen  & Jean-Jacques Strodiot  & 

  2. Institut de Mathématiques (B37), University of Liège, Grande Traverse 12, 4000, Liège, Belgium

    Patricia Tossings

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© 2000 Springer-Verlag Berlin Heidelberg

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Ferris, M.C., Sinapiromsaran, K. (2000). Formulating and Solving Nonlinear Programs as Mixed Complementarity Problems. In: Nguyen, V.H., Strodiot, JJ., Tossings, P. (eds) Optimization. Lecture Notes in Economics and Mathematical Systems, vol 481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57014-8_10

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  • DOI: https://doi.org/10.1007/978-3-642-57014-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66905-0

  • Online ISBN: 978-3-642-57014-8

  • eBook Packages: Springer Book Archive

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