Abstract
A triangulation of the nonnegative orthant and a special labeling of the vertices lead to a combinatorial procedure for seeking solutions or approximate solutions to the nonlinear complementarity problem under coercive-like assumptions on the problem functions. Derivatives are not required. Convergence is proved, computational considerations are discussed, and some preliminary applications to convex programming and saddle point computation, along with numerical results, are presented.
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The work of this author was sponsored in part by National Science Foundation grant GJ-1154X to the National Bureau of Economic Research, Inc., while the author was a Research Associate at the National Bureau's Computer Research Center for Economics and Management Science of Cambridge, Mass.
The work of this author was sponsored in part by the Office of Naval Research, Contract No. N000-14-67-A-0321-0003 (NR-047-085).
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Fisher, M.L., Gould, F.J. A simplicial algorithm for the nonlinear complementarity problem. Mathematical Programming 6, 281–300 (1974). https://doi.org/10.1007/BF01580246
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DOI: https://doi.org/10.1007/BF01580246