Abstract
A Newton-type algorithm has been presented elsewhere for solving non-linear inequalities of the formf(x)≦0,g(x)=0, and quadratic convergence has been proved under very strong hypotheses. In this paper we show that the same results hold under a considerable weakening of the hypotheses.
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Daniel, J. W.: On perturbations in systems of linear inequalities. SIAM J. Numer. Anal.10, 299–307 (1973). Also appeared as CNA-50, Center for Numerical Analysis, UT-Austin (1972)
Pshenichnyi, B. N.: Newton's method for the solution of systems of equalities and inequalities. Mat. Zametki8, 635–640; translated in Math. Notes8, 827–830 (1970)
Robinson, S. M.: Bounds for error in the solution set of a perturbed linear program. J. Lin. Alg. Appl.6, 69–82 (1972a)
Robinson, S. M.: Normed convex processes. Trans. Am. Math. Soc.174, 127–140 (1972b). Also appeared as Tech. Sum. Report 1135, Math. Res. Center, U. of Wisconsin, 1971
Robinson, S. M.: Extension of Newton's method to nonlinear functions with values in a cone. Numer. Math.19, 341–347 (1972c). Also appeared as Tech. Sum. Report 1161, Math. Res. Center, U. of Wisconsin, 1971
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This research was supported in part by contract number N00014-67-A-0126-0015, NR 044-425, from the Office of Naval Research.
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Daniel, J.W. Newton's method for nonlinear inequalities. Numer. Math. 21, 381–387 (1973). https://doi.org/10.1007/BF01436488
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DOI: https://doi.org/10.1007/BF01436488