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<p>In this paper, we propose improved versions of the Hestenes-Stiefel and Polak-Ribière-Polyak methods for addressing unconstrained optimization problems. Specifically, while preserving their excellent numerical performance, we introduce newly designed adaptive restart mechanism to improve the theoretical performance of these classical conjugate gradient methods. For each improved method, we ensure that the corresponding search direction is independent of any line search and has sufficient descent condition and the trust region property. Under general conditions, including the application of an Armijo line search for step size determination, we establish the theoretical convergence and iterative complexity of the improved methods. To show their effectiveness, we tested them on at least 100 unconstrained optimization problems.</p>

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Two adaptive restarting improved conjugate gradient methods with iterative complexity guarantees

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Kai Wang,
  • Jinhu Chen,
  • Pengjie Liu,
  • Bohan Li

摘要

In this paper, we propose improved versions of the Hestenes-Stiefel and Polak-Ribière-Polyak methods for addressing unconstrained optimization problems. Specifically, while preserving their excellent numerical performance, we introduce newly designed adaptive restart mechanism to improve the theoretical performance of these classical conjugate gradient methods. For each improved method, we ensure that the corresponding search direction is independent of any line search and has sufficient descent condition and the trust region property. Under general conditions, including the application of an Armijo line search for step size determination, we establish the theoretical convergence and iterative complexity of the improved methods. To show their effectiveness, we tested them on at least 100 unconstrained optimization problems.