A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations View Full Text


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Article Info

DATE

2016-01

AUTHORS

Gonglin Yuan, Zehong Meng, Yong Li

ABSTRACT

It is well known that nonlinear conjugate gradient methods are very effective for large-scale smooth optimization problems. However, their efficiency has not been widely investigated for large-scale nonsmooth problems, which are often found in practice. This paper proposes a modified Hestenes–Stiefel conjugate gradient algorithm for nonsmooth convex optimization problems. The search direction of the proposed method not only possesses the sufficient descent property but also belongs to a trust region. Under suitable conditions, the global convergence of the presented algorithm is established. The numerical results show that this method can successfully be used to solve large-scale nonsmooth problems with convex and nonconvex properties (with a maximum dimension of 60,000). Furthermore, we study the modified Hestenes–Stiefel method as a solution method for large-scale nonlinear equations and establish its global convergence. Finally, the numerical results for nonlinear equations are verified, with a maximum dimension of 100,000. More... »

PAGES

129-152

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    http://scigraph.springernature.com/pub.10.1007/s10957-015-0781-1

    DOI

    http://dx.doi.org/10.1007/s10957-015-0781-1

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1025429810


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