پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 41 |
| تعداد شمارهها | 1,100 |
| تعداد مقالات | 9,434 |
| تعداد مشاهده مقاله | 17,002,936 |
| تعداد دریافت فایل اصل مقاله | 11,927,528 |
Efficient Solution of Nonlinear Unconstraint Optimization Problems using Quasi-Newton's Method: A Revised Approach | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 3، دوره 9، شماره 1، مرداد 2024، صفحه 49-65 اصل مقاله (510.25 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2023.64138.1204 | ||
| نویسنده | ||
| Hajar Alimorad* | ||
| Department of Mathematics, Jahrom University, Jahrom, P.O. Box 74135-111, Iran | ||
| چکیده | ||
| While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems. Newton's method, a notable numerical technique within the category of line search algorithms, is widely used for function optimization. The search direction and step length play crucial roles in this algorithm. This paper introduces an algorithm aimed at enhancing the step length within the Broyden quasi-Newton process. Additionally, numerical examples are provided to compare the effectiveness of this new method with another approach. | ||
| کلیدواژهها | ||
| Optimization؛ Hessian matrix؛ Quasi-Newton method؛ Constrained and unconstrained problems | ||
| مراجع | ||
|
[1] Andrei, N. (2008). “An unconstrained optimization test functions collection”, Advanced Modeling and Optimization, 10(1), 147-161.
[2] Broyden, C. (1965). “A class of methods for solving nonlinear simultaneous equations”, Mathematics of Computation, 19, 577-593.
[3] Dehghan, T., Niri, M., Hosseini, M., Heydari, M. (2019). “An efficient improvement of the Newton’s method for solving non-convex optimization problems”, Computational Methods for Differential Equations, 7(1), 69-85.
[4] Dennis, J.E., Schnabel, R.B. (1993). “Numerical methods for unconstrained optimization and non-linear equations”, SIAM, Philadelphia.
[5] Fang, X.W., Ni, Q., Zeng, M.L. (2018). “A modified quasi-Newton’s method for nonlinear equations”, Journal of Computational and Applied Mathematics, 328, 44-58.
[6] Li, D.H., Fukushima, M., Qi, L., Yamashita, N. (2004). “Regularized Newton methods for convex minimization problems with singular solutions”, Computational Optimization and Applications, 28, 131-147.
[7] Narcowich, F.J. (2023). “The Rank of a Matrix”, https://www.math.tamu.edu/~fnarc/psfiles/rank2005.pdf.
[8] Polyak, R.A. (2009). “Regularized Newton’s method for unconstrained convex optimization”, Mathematical Programming, 120, 125-145.
[9] Sa, H., Chen, G.Q., Sui, Y.K., Wu, C.Y. (2016). “A new newton-like method for solving nonlinear equations”, Springer Plus., 5, 12-69.
[10] Shen, Ch., Xiongda, Ch., Liang, Y. (2012). “A regularized Newton’s method for degenerate unconstrained optimization problems”, Optimization Letters, 6, 1913-1933.
[11] Song, W.u., Haijun, W. (2020). “A modified Newton-like method for nonlinear equations”, Computational and Applied Mathematics, 39, 238.
[12] Sui, Y., Sa, H., Chen, G. (2014). “An improvement for the rational approximation RALND at accumulated two-point information”, Mathematica Numerica Sinica, 36, 51-64.
[13] Ueda, K., Yamashita, N. (2010). “Convergence properties of the regularized Newton’s method for the unconstrained non-convex optimization”, Applied Mathematics and Optimization, 62, 27-46.
[14] Yuan, G., Wang, Zh., Li, P. (2022). “Global convergence of a modified Broyden family method for non-convex functions”, Journal of Industrial and Management Optimization, 18(6), 4393-4407.
[15] Zhou, G., Toh, K.C. (2005). “Superlinear convergence of a Newton-type algorithm for monotone equations”, Journal of Optimization Theory and Applications, 125, 205-221. | ||
|
آمار تعداد مشاهده مقاله: 137 تعداد دریافت فایل اصل مقاله: 48 |
||