Global convergence in infeasible-interior-point algorithms |
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Authors: | Kojima Masakazu Noma Toshihito Yoshise Akiko |
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Affiliation: | (1) Department of Information Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, 152 Tokyo, Japan;(2) Ships Division, Equipment Bureau, Defense Agency, Minato-ku, 102 Tokyo, Japan;(3) Institute of Socio-Economic Planning, University of Tsukuba, 305 Tsukuba, Ibaraki, Japan |
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Abstract: | This paper presents a wide class of globally convergent interior-point algorithms for the nonlinear complementarity problem with a continuously differentiable monotone mapping in terms of a unified global convergence theory given by Polak in 1971 for general nonlinear programs. The class of algorithms is characterized as: Move in a Newton direction for approximating a point on the path of centers of the complementarity problem at each iteration. Starting from a strictly positive but infeasible initial point, each algorithm in the class either generates an approximate solution with a given accuracy or provides us with information that the complementarity problem has no solution in a given bounded set. We present three typical examples of our interior-point algorithms, a horn neighborhood model, a constrained potential reduction model with the use of the standard potential function, and a pure potential reduction model with the use of a new potential function.Research supported in part by Grant-in-Aids for Co-Operative Research (03832017) of the Japan Ministry of Education, Science and Culture.Corresponding author. |
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Keywords: | Monotone complementarity problem Interior-point algorithm Potential reduction algorithm Infeasibility Global convergence |
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