Journal of Optimization Theory and Applications

, Volume 180, Issue 3, pp 993–1010

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

• María de los Ángeles Martínez
• Damián Fernández
Article

## 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

## Notes

### Acknowledgements

This work was partially supported by FONCyT Grant PICT 2014-2534 and CONICET Grant PIP 112-201101-00050.

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