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|Title:||Superlinear convergence of a Newton-type algorithm for monotone equations|
|Source:||Zhou, G., Toh, K.C. (2005-04). Superlinear convergence of a Newton-type algorithm for monotone equations. Journal of Optimization Theory and Applications 125 (1) : 205-221. ScholarBank@NUS Repository. https://doi.org/10.1007/s10957-004-1721-7|
|Abstract:||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. © 2005 Springer Science+Business Media, Inc.|
|Source Title:||Journal of Optimization Theory and Applications|
|Appears in Collections:||Staff Publications|
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