Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations
Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations
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DOI：
10.1007/s10957-004-1721-7
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发表时间：
2005-04
影响因子：
1.9
通讯作者：
Guanglu Zhou;K. Toh
中科院分区：
文献类型：
--
作者：
Guanglu Zhou;K. Toh
We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs.
