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Topographical Estimation of Visual Population Receptive Fields by fMRI
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A modified filter nonmonotone adaptive retrospective trust region method.

Xianfeng Ding1,2, Quan Qu1, Xinyi Wang1

  • 1School of Sciences, Southwest Petroleum University, Chengdu, China.

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|June 17, 2021
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Summary

A new nonmonotone adaptive trust region method improves unconstrained optimization. This robust algorithm enhances trial step acceptance and shows global and superlinear convergence.

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Area of Science:

  • Numerical Analysis
  • Optimization Theory

Background:

  • Unconstrained optimization problems are fundamental in applied mathematics and computational science.
  • Existing trust region methods face challenges with convergence and step acceptance rates.

Purpose of the Study:

  • To introduce a novel nonmonotone adaptive retrospective trust region line search method.
  • To enhance the efficiency and robustness of algorithms for unconstrained optimization.

Main Methods:

  • Utilizing a multidimensional filter technique to improve trial step acceptance probability.
  • Developing a new nonmonotone trust region ratio based on a convex combination.
  • Analyzing global and superlinear convergence properties.

Main Results:

  • The proposed method demonstrates increased acceptance probability for trial steps.
  • The algorithm achieves proven global and superlinear convergence under specific conditions.
  • Comparative numerical experiments confirm the method's effectiveness and robustness.

Conclusions:

  • The new nonmonotone adaptive retrospective trust region method is effective for unconstrained optimization.
  • The technique offers improved performance and reliability compared to existing approaches.