Adjusting the BFGS update for quasi-Newton methods
*Basim A. HassanCorresponding authorbasimah@uomosul.edu.iqbasimabas39@gmail.comDepartment of MathematicsCollege of Computers Sciences and MathematicsUniversity of MosulMosul, 41002, Iraq0000-0003-3510-9818View full profile → , Ahmed W. Mohammedahmed1988st@gmail.comDepartment of MathematicsCollege of Computers Sciences and MathematicsUniversity of MosulMosul, 41002, Iraq0009-0003-5460-6323View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Jun 2024
- Published Online:
- 13 Feb 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1772
- Pages:
- 31–41
Abstract
Keywords
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References
[1] R. Fletcher. Practical Method of Optimization, 2nd Edition. New York (1989).
[2] P. Wolfe. Convergence Conditions for Ascent Methods. SIAM Review, vol. 11, no. 2 (1969). https://doi.org/10.1137/1011036.
[3] G. Yuan, Z. Wei and Y. Wu. Modified limited memory BFGS method with nonmonotone line search for unconstrained optimization. Journal of the Korean Mathematical Society, vol. 47, no. 4 (2010). https://doi.org/10.4134/JKMS.2010.47.4.767.
[4] R. H. Byrd and J. Nocedal. A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization. SIAM J Numer Anal, vol. 26, no. 3 (1989). https://doi.org/10.1137/0726042.
[5] G. Yuan and Z. Wei. Convergence analysis of a modified BFGS method on convex minimizations. Comput Optim Appl, vol. 47, no. 2 (2010). https://doi.org/10.1007/s10589-008-9219-0.
[6] J. Nocedal and S. Wright, Numerical optimization, series in operations research and financial engineering (2006).
[7] J. Z. Zhang, N. Y. Deng and L. H. Chen. New quasi-Newton equation and related methods for unconstrained optimization. J Optim Theory Appl, vol. 102, no. 1 (1999). https://doi.org/10.1023/A:1021898630001.
[8] M. J. D. Powell. Algorithms for nonlinear constraints that use lagrangian functions. Math Program, vol. 14, no. 1 (1978). https://doi.org/10.1007/BF01588967.
[9] D. H. Li and M. Fukushima. A modified BFGS method and its global convergence in nonconvex minimization. J Comput Appl Math, vol. 129, no. 1–2 (2001). https://doi.org/10.1016/S0377-0427(00)00540-9.
[10] Z. Wei, G. Li and L. Qi. New quasi-Newton methods for unconstrained optimization problems. Appl Math Comput, vol. 175, no. 2 (2006). https://doi.org/10.1016/j.amc.2005.08.027.
[11] B. A. Hassan. A new type of quasi-newton updating formulas based on the new quasi-newton equation. Numerical Algebra, Control and Optimization, vol. 10, no. 2 (2020). https://doi.org/10.3934/naco.2019049.
[12] B. A. Hassan and M. W. Taha. A new variants of quasi-newton equation based on the quadratic function for unconstrained optimization. Indonesian Journal of Electrical Engineering and Computer Science, vol. 19, no. 2 (2020). https://doi.org/10.11591/ijeecs.v19.i2.pp701-708.
[13] B. A. Hassan and G. M. Al-Naemi. A new quasi-newton equation on the gradient methods for optimization minimization problem. Indonesian Journal of Electrical Engineering and Computer Science, vol. 19, no. 2 (2020). https://doi.org/10.11591/ijeecs.v19.i2.pp737-744.
[14] B. A. Hassan and R. M. Sulaiman. Using a New Type Quasi-Newton Equation for Unconstrained Optimization. in Proceedings of the 7th International Engineering Conference “Research and Innovation Amid Global Pandemic”, IEC 2021 (2021). doi:10.1109/IEC52205.2021.9476089.
[15] B. A. Hassan and I. A. R. Moghrabi. A modified secant equation quasi-Newton method for unconstrained optimization. J Appl Math Comput, vol. 69, no. 1 (2023). https://doi.org/10.1007/s12190-022-01750-x.
[16] B. A. Hassan and A. R. Ayoob. An Adaptive Quasi-Newton Equation for Unconstrained Optimization. in Proceedings of 2021 2nd Information Technology to Enhance E-Learning and other Application Conference, IT-ELA 2021 (2021). doi:10.1109/IT-ELA52201.2021.9773580.
[17] Basim A. Hassan and Abdulrahman R. Ayoob. On the New Quasi-Newton Equation for Unconstrained Optimization. 8th IEC 2022-International Engineering Conference: Towards Engineering Innovations and Sustainability (2022).
[18] Z. H. Abdulabbas and L. A. R. Al Asadi, “Calculating Dynamic Strengths of Concrete Subjected to Impact Load,” Key Engineering Materials, vol. 895, pp. 12–19 (Aug. 2021), doi: https://doi.org/10.4028/www.scientific.net/kem.895.12.
[19] X. Fang, Q. Ni and M. Zeng. A modified quasi-Newton method for nonlinear equations. J Comput Appl Math, vol. 328 (2018). https://doi.org/10.1016/j.cam.2017.06.024.
[20] G. Yuan, Z. Wei and X. Lu. Global convergence of BFGS and PRP methods under a modified weak Wolfe–Powell line search. Appl Math Model, vol. 47 (2017). https://doi.org/10.1016/j.apm.2017.02.008.
[21] G. Yuan, Z. Sheng, B. Wang, W. Hu and C. Li. The global convergence of a modified BFGS method for nonconvex functions. J Comput Appl Math, vol. 327 (2018). https://doi.org/10.1016/j.cam.2017.05.030.
[22] L. A. R. Al Asadi, H. S. Al Bahrani, and L. K. Al Waeli, “Parametric Study for Design and Analysis of Box Culvert by Using Newton’s-Raphson Method and MATLAB Software,” Key Engineering Materials, vol. 870, pp. 11–19 (Oct. 2020), doi: https://doi.org/10.4028/www.scientific.net/kem.870.11.
[23] J. J. Moré, B. S. Garbow and K. E. Hillstrom. Testing Unconstrained Optimization Software. ACM Transactions on Mathematical Software (TOMS), vol. 7, no. 1 (1981). https://doi.org/10.1145/355934.355936.
[24] W. Gao and M. R. Farahani. The hyper-zagreb index for an infinite family of nanostar dendrimer,” J. Discrete Math. Sci. Cryptography, vol. 20, no. 2, pp. 2017. https://doi.org/10.1080/09720529.2016.1220088.
[25] W. Gao, L. Shi and M. R. Farahani. Szeged Related Indices of TUAC6[p, q],” J. Discrete Math. Sci. Cryptography, vol. 20, no. 2, pp. 2017. https://doi.org/10.1080/09720529.2016.1228312.
[26] M. Imran, A. A. E. Abunamous, D. Adi, S. H. Rafique, A. Q. Baig and M. R. Farahani. Eccentricity based topological indices of honeycomb networks,” J. Discrete Math. Sci. Cryptography, vol. 22, no. 7, pp. 2019. https://doi.org/10.1080/09720529.2019.1691326.
[27] M. N. Jahangeer Baig, C. Y. Jung, N. Ahmad and S. M. Kang. On the M-polynomials and degree-based topological indices of an important class of graphs,” J. Discrete Math. Sci. Cryptography, vol. 22, no. 7, pp. 2019. https://doi.org/10.1080/09720529.2019.1691327.
[28] S. S. Alamoti, M. Alaeiyan and A. Gilani. Studying thermodynamic properties of linear acenes molecules (C4n+2H2n+4) using hyper-Zagreb index,” J. Discrete Math. Sci. Cryptography, vol. 22, no. 7, pp. 2019. https://doi.org/10.1080/09720529.2019.1694258.
[29] Y. Yuan and W. Sun. Theory and Methods of Optimization. Science Press of China, no. Beijing (1999).
[30] M. A. Mustafa, S. M. A. Nayeem, M. A. Khan, and S. A. Mollah, “A novel fuzzy M-transform technique for sustainable ground water level prediction,” Applied Geomatics, vol. 16, no. 1, pp. 9–15 (Jan. 2023), doi: https://doi.org/10.1007/s12518-022-00486-4.
[31] S. Kadham and A. Alkiffai, “Model Tumor Response to Cancer Treatment Using Fuzzy Partial SH-Transform: An Analytic Study,” International Journal of Mathematics and Computer Science, vol. 18, no. 1, pp. 23–28 (2022), Available: https://future-in-tech.net/18
[32] S. M. Kadham, M. A. Mustafa, N. K. Abbass, and S. Karupusamy, “IoT and artificial intelligence–based fuzzy-integral N-transform for sustainable groundwater management,” Applied Geomatics (Dec. 2022), doi: https://doi.org/10.1007/s12518-022-00479-3.
[33] S. M. Kadham, “Acute interstitial pneumonia image enhancement using fuzzy partial transforms,” Applied Geomatics, vol. 16, no. 1, pp. 35–39 (May 2023), doi: https://doi.org/10.1007/s12518-023-00509-8.




