On the Local and Superlinear Convergence of a Secant Modified Linear-Programming-Newton Method

María de los Ángeles Martínez () and Damián Fernández ()
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María de los Ángeles Martínez: Universidad Nacional de Córdoba
Damián Fernández: Universidad Nacional de Córdoba

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 3, No 16, 993-1010

Abstract: Abstract We present a superlinearly convergent method to solve a constrained system of nonlinear equations. The proposed procedure is an adaptation of the linear-programming-Newton method replacing the first-order information with a secant update. Thus, under mild assumptions, the method is able to find possible nonisolated solutions without computing any derivative and achieving a local superlinear rate of convergence. In addition to the convergence analysis, some numerical examples are presented in order to show the fulfillment of the expected rate of convergence.

Keywords: Constrained nonlinear system of equations; Nonisolated solutions; Quasi-Newton method; Local superlinear convergence; 90C30; 65K05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1407-1

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