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Modified Three-Term Liu–Storey Conjugate Gradient Method for Solving Unconstrained Optimization Problems and Image Restoration Problems

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  • Yulun Wu
  • Mengxiang Zhang
  • Yan Li

Abstract

A new three-term conjugate gradient method is proposed in this article. The new method was able to solve unconstrained optimization problems, image restoration problems, and compressed sensing problems. The method is the convex combination of the steepest descent method and the classical LS method. Without any linear search, the new method has sufficient descent property and trust region property. Unlike previous methods, the information for the function is assigned to . Next, we make some reasonable assumptions and establish the global convergence of this method under the condition of using the modified Armijo line search. The results of subsequent numerical experiments prove that the new algorithm is more competitive than other algorithms and has a good application prospect.

Suggested Citation

  • Yulun Wu & Mengxiang Zhang & Yan Li, 2020. "Modified Three-Term Liu–Storey Conjugate Gradient Method for Solving Unconstrained Optimization Problems and Image Restoration Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-20, October.
    • Handle: RePEc:hin:jnlmpe:7859286
    DOI: 10.1155/2020/7859286
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