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An enhanced BFGS framework with nonmonotone line search for nonconvex unconstrained optimization | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 28 مهر 1405 اصل مقاله (371.88 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.34273.3179 | ||
| نویسندگان | ||
| Parisa Ostovari؛ Keyvan Amini* | ||
| Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, Iran | ||
| چکیده | ||
| Quasi-Newton methods constitute an important class of iterative techniques for solving unconstrained optimization problems, with the BFGS method being one of the most successful and widely used members of this class. Despite its well-established effectiveness in solving nonlinear unconstrained optimization problems, the BFGS algorithm still suffers from several limitations that may affect its computational efficiency and performance, particularly for large-scale problems. First, the direction generated by the BFGS method may fail to be a descent direction, particularly when the condition s_k^T y_k > 0 fails to hold. Consequently, the positive definiteness of the matrix B_k cannot be guaranteed. Second, although global and superlinear convergence results have been established for convex optimization problems, these results do not necessarily hold for general problems. In this paper, we propose a new modified BFGS method with nonmonotone line search for solving nonconvex unconstrained optimization problems, where the approximate Hessian matrix is updated based on a modified secant condition and an adaptive scaling parameter. It is shown that the search direction is a descent direction independently of the line search. The global convergence of the proposed method has been established under certain standard assumptions, without assuming convexity of the objective function. We also report some numerical experiments to demonstrate the efficiency of the proposed method. | ||
| کلیدواژه‌ها | ||
| Unconstrained optimization؛ quasi-Newton method؛ modified BFGS method؛ nonmonotone line search؛ global convergence | ||
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آمار تعداد مشاهده مقاله: 6 تعداد دریافت فایل اصل مقاله: 7 |
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