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<p>Whether the BFGS method is globally convergent under weak Wolfe-Powell (WWP) line search is a question of wide interest in recent years. For convex functions, the BFGS method is easily proved to have global convergence, but for nonconvex functions in general, the BFGS method does not have global convergence. Therefore, we propose an improved BFGS algorithm with global convergence, which has the following properties: (i) the iterative direction is modified so that the modified direction satisfies the special descent condition; (ii) the assumption for proving global convergence are weakened and the proof procedure is given in detail; the improved BFGS algorithm is globally convergent for general functions, and it has a wider application range. Meanwhile, numerical experiments also show that our algorithm has good performance.</p>

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Modified BFGS algorithm with particular descent condition for nonconvex functions

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Xiangli Li,
  • Binglan Li,
  • Zhiling Wang

摘要

Whether the BFGS method is globally convergent under weak Wolfe-Powell (WWP) line search is a question of wide interest in recent years. For convex functions, the BFGS method is easily proved to have global convergence, but for nonconvex functions in general, the BFGS method does not have global convergence. Therefore, we propose an improved BFGS algorithm with global convergence, which has the following properties: (i) the iterative direction is modified so that the modified direction satisfies the special descent condition; (ii) the assumption for proving global convergence are weakened and the proof procedure is given in detail; the improved BFGS algorithm is globally convergent for general functions, and it has a wider application range. Meanwhile, numerical experiments also show that our algorithm has good performance.