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A derivative-free iterative method for nonlinear monotone equations with convex constraints

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Abstract

In this paper, based on the projection strategy, we propose a derivative-free iterative method for large-scale nonlinear monotone equations with convex constraints, which can generate a sufficient descent direction at each iteration. Due to its lower storage and derivative-free information, the proposed method can be used to solve large-scale non-smooth problems. The global convergence of the proposed method is proved under the Lipschitz continuity assumption. Moreover, if the local error bound condition holds, the proposed method is shown to be linearly convergent. Preliminary numerical comparison shows that the proposed method is efficient and promising.

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Funding

This research was partially supported by Chongqing Research Program of Basic Research and Frontier Technology (Grant number:cstc2017jcyjAX0318), Program for Innovation Team Building at Institutions of Higher Education in Chongqing (Grant number:CXTDX201601035), and Chongqing Municipal Key Laboratory of Institutions of Higher Education (Grant No. [2017]3). The fund of Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant number:KJQN20180120).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, China

    Jinkui Liu

  2. Key Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, China

    Jinkui Liu & Yuming Feng

Authors
  1. Jinkui Liu
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  2. Yuming Feng
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Correspondence to Jinkui Liu.

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Liu, J., Feng, Y. A derivative-free iterative method for nonlinear monotone equations with convex constraints. Numer Algor 82, 245–262 (2019). https://doi.org/10.1007/s11075-018-0603-2

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  • DOI: https://doi.org/10.1007/s11075-018-0603-2

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