Abstract
In the theory of fixed points and complementarity, several methods have been developed for solving systems of nonlinear equations F(x)=0, where F:X→R n is continuous and X is an n-dimensional polyhedron. This paper deals with the case where the mapping F is separable, and gives two kinds of piecewise linear homotopies with some separable structure. Comparisons in this paper confirm that the separable homotopies will bring about much increase of computational efficiency in the homotopic approach to systems of equations with separable mappings.
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© 1978 The Mathematical Programming Society
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Kojima, M. (1978). On the homotopic approach to systems of equations with separable mappings. In: Balinski, M.L., Cottle, R.W. (eds) Complementarity and Fixed Point Problems. Mathematical Programming Studies, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120789
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DOI: https://doi.org/10.1007/BFb0120789
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