Open AccessThe parameter-Newton iteration for the second-order cone linear complementarity problem
Author(s) -
Peng Zhou,
Teng Wang
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022076
Subject(s) - newton's method , mathematics , nonlinear system , complementarity (molecular biology) , quadratic equation , bisection method , local convergence , convergence (economics) , steffensen's method , rate of convergence , iterative method , mathematical analysis , mathematical optimization , key (lock) , newton's method in optimization , computer science , geometry , physics , genetics , quantum mechanics , economics , biology , economic growth , computer security
In this paper, we propose the parameter-Newton (PN) method to solve the second-order linear complementarity problem (SOCLCP). The key idea of PN method is that we transfer the SOCLCP into a system of nonlinear equations by bringing in a parameter. Then we solve the system of nonlinear equations by Newton method. At last, we prove that the PN method has quadratic convergence. Compared with the bisection-Newton (BN) method, the PN method has less CPU time and higher accuracy in numerical tests.