Abstract
Homotopy methods are well known techniques for computing a root of a nonlinear function. By extending the setup of Eaves and Scarf [1] to the nonlinear case a homotopy method, in the spirit of Keller’s [2], is developed to compute roots of continuous piecewise differentiable functions. The motivation of this work is to elaborate homotopy algorithms for solving nonlinear programming problems. The application of the results, given in this paper, to optimization problems will be published elsewhere.
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5. References
B.C. Eaves and H. Scarf (1976). "The solution of Systems of Piecewise Linear Equations". Mathematics of Operations Research, Vol. 1, No 1, 1–31.
Keller, H.B. (1979). "Global Homotopies and Newton Methods". Recent Advances in Numerical Analysis. Academic Press, New York.
Robinson S. M. (1979). "Generalized Equations and Their Solutions, Part I: Basic Theory". Math. Programming Studies 10, 128–141
Smale, S. (1976). "A convergent Process of Price Adjustment and Global Newton Methods". J. of Mathemtical Economics 3, 107–120.
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© 1983 Springer-Verlag
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Lentini, M., Reinoza, A. (1983). Piecewise nonlinear homotopies. In: Numerical Methods. Lecture Notes in Mathematics, vol 1005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0112533
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DOI: https://doi.org/10.1007/BFb0112533
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