Abstract
This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations.
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Partially supported by the Sakkokai Foundation and by the Grand-in-Aid for Scientific Research of the Ministry of Education and Culture No. 58750265.
Partially supported by the Grant-in-Aid for Scientific Research of the Ministry of Education and Culture No. 56460103.
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Kojima, M., Oishi, S., Sumi, Y. et al. A PL homotopy continuation method with the use of an odd map for the artificial level. Mathematical Programming 31, 235–244 (1985). https://doi.org/10.1007/BF02591752
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DOI: https://doi.org/10.1007/BF02591752