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A derivative-free memoryless BFGS hyperplane projection method for solving large-scale nonlinear monotone equations

Abstract

In this work, by combining a three-term memoryless BFGS conjugate gradient direction with the hyperplane projection technique , we develop a new derivative-free algorithm to solve nonlinear monotone equations. The method is motivated by conjugate gradient method and hyperplane projection, as well as quasi-Newton method. The search direction has three terms and is obtained by modifying the BFGS updating matrix with a unit matrix in each step. The algorithm needs no matrices computing, and it is suitable for solving large-scale nonlinear monotone equations. The proposed method satisfies the Dai–Liao conjugacy conditions and is always descent irrelative to any line searches. Under standard conditions, the optimizer solution can be obtained by a globally convergent sequence as long as the initial point is given. The reported numerical experiments show that the method is promising and efficient compared to similar algorithms in the literature.

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Funding

This work is supported by National Natural Science Foundation of China (Grant Number: 51535012 and 71671190).

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Correspondence to Songhai Deng.

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Huang, F., Deng, S. & Tang, J. A derivative-free memoryless BFGS hyperplane projection method for solving large-scale nonlinear monotone equations. Soft Comput 27, 3805–3815 (2023). https://doi.org/10.1007/s00500-022-07536-4

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  • DOI: https://doi.org/10.1007/s00500-022-07536-4

Keywords

  • Nonlinear monotone equations
  • Derivative-free method
  • Hyperplane projection method
  • Conjugate gradient method