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.
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Acknowledgements
This work was partially supported by FONCyT Grant PICT 2014-2534 and CONICET Grant PIP 112-201101-00050.
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Communicated by Alexey F. Izmailov.
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Martínez, M.Á., Fernández, D. On the Local and Superlinear Convergence of a Secant Modified Linear-Programming-Newton Method. J Optim Theory Appl 180, 993–1010 (2019). https://doi.org/10.1007/s10957-018-1407-1
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DOI: https://doi.org/10.1007/s10957-018-1407-1
Keywords
- Constrained nonlinear system of equations
- Nonisolated solutions
- Quasi-Newton method
- Local superlinear convergence