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<p>The conjugate gradient method is among the most effective approaches for solving large-scale unconstrained optimization problems. Within this class, the Hestenes–Stiefel method demonstrates strong numerical performance, although its global convergence properties are limited. This paper presents a new Hestenes–Stiefel-type conjugate gradient method (NHS*) and compares it against the VHS algorithm on benchmark problems, employing identical Wolfe line search parameters and stopping criteria. Performance profiles are generated for iteration count, CPU time, and gradient norm. Numerical results indicate that NHS* is generally more efficient in terms of iteration count, whereas VHS achieves superior computation time, with both methods yielding comparable final gradient norms. Overall, NHS* offers a distinct numerical advantage for large-scale unconstrained optimization.</p>

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A New Hestenes–Stiefel-Type Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problems

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Yuan Jin,
  • Guangyun Xu,
  • Liang Chen

摘要

The conjugate gradient method is among the most effective approaches for solving large-scale unconstrained optimization problems. Within this class, the Hestenes–Stiefel method demonstrates strong numerical performance, although its global convergence properties are limited. This paper presents a new Hestenes–Stiefel-type conjugate gradient method (NHS*) and compares it against the VHS algorithm on benchmark problems, employing identical Wolfe line search parameters and stopping criteria. Performance profiles are generated for iteration count, CPU time, and gradient norm. Numerical results indicate that NHS* is generally more efficient in terms of iteration count, whereas VHS achieves superior computation time, with both methods yielding comparable final gradient norms. Overall, NHS* offers a distinct numerical advantage for large-scale unconstrained optimization.