Abstract
A general framework of potential reduction methods is proposed for solving the nonlinear complementarity problem NCP(F). It is shown that this class of methods not only cover the traditional potential reduction methods, but also generate new methods which have not appeared before. The interesting feature is that we generalize the Hadamard product x o y in the commonly used formulation: F(x) - y = 0, x o y = 0, x ≥ 0, y ≥ 0, when transforming the nonlinear complementarity problem into a simply constrained system of equations. Global convergence is established under no more than the standard assumptions. Stronger convergence results are proved when special reformulations are considered.
This work was supported by the Australian Research Council. Most of this owrk was carried out when the author was in the Department of Mathematics and Statistics, The University of Melbourne.
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© 1999 Kluwer Academic Publishers
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Jiang, H. (1999). Potential Reduction Methods for the Nonlinear Complementarity Problem. In: Progress in Optimization. Applied Optimization, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3285-5_9
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DOI: https://doi.org/10.1007/978-1-4613-3285-5_9
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