On the Local and Superlinear Convergence of a Secant Modified Linear-Programming-Newton Method
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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.
KeywordsConstrained nonlinear system of equations Nonisolated solutions Quasi-Newton method Local superlinear convergence
Mathematics Subject Classification90C30 65K05
This work was partially supported by FONCyT Grant PICT 2014-2534 and CONICET Grant PIP 112-201101-00050.
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