A Quadratic Model based Conjugate Gradient Optimization Method

f4da806a-7992-4373-892d-190ce6ed87bd20231206110235000wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=4051919202291920222210.37394/23206.2023.22https://wseas.com/journals/mathematics/2023.phpA Quadratic Model based Conjugate Gradient Optimization MethodIsam H.HalilDepartment of Mathematics, College of Science, Kirkuk University, Kirkuk, IRAQIssam A.R.MoghrabiDepartment of Computer Science, College of Arts and Sciences, University Central Asia, Naryn, KYRGYZ REPUBLICAhmed A.FawzeDepartment of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, IRAQBasim A.HassanDepartment of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, IRAQHisham M.KhudhurDepartment of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, IRAQIn this paper, we introduce a nonlinear scaled conjugate gradient method, operating on the premise of a descent and conjugacy relationship. The proposed algorithm employs a conjugacy parameter that is determined to ensure that the method generates conjugate directions. It also utilizes a parameter that scales the gradient to enhance the convergence behavior of the method. The derived method not only exhibits the crucial feature of global convergence but also maintains the generation of descent directions. The efficiency of the method is established through numerical tests conducted on a variety of high-dimensional nonlinear test functions. The obtained results attest to the improved behavior of the derived algorithm and support the presented theory.12620231262023925930101https://wseas.com/journals/mathematics/2023/c065106-052(2023).pdf10.37394/23206.2023.22.101https://wseas.com/journals/mathematics/2023/c065106-052(2023).pdf10.1007/s101070100263E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Math. Program. Ser. B, vol. 91, no. 2, pp. 201–213, 2002, doi: 10.1007/s101070100263. 10.11591/ijeecs.v29.i3.pp1438-1445B. A. Hassan and H. A. Alashoor, “On image restoration problems using new conjugate gradient methods,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 29, no. 3, p. 1438, Mar. 2023, doi: 10.11591/ijeecs.v29.i3.pp1438-1445. 10.1504/ijmmno.2023.132286H. M. Khudhur and A. A. M. Fawze, "An improved conjugate gradient method for solving unconstrained optimization and image restoration problems," Int. J. Mathematical Modeling Numerical Optimization, vol. 13, no. 3, pp. 313–325, 2023, doi: 10.1504/IJMMNO.2023.132286. 10.29020/nybg.ejpam.v15i4.4568B. A. Hassan and H. Sadiq, “Efficient New Conjugate Gradient Methods for Removing Impulse Noise Images,” Eur. J. Pure Appl. Math., vol. 15, no. 4, pp. 2011–2021, Oct. 2022, doi: 10.29020/nybg.ejpam.v15i4.4568. 10.2139/ssrn.4569182S. Aji, A. B. Abubakar, A. I. Kiri, and A. Ishaku, “A Spectral Conjugate Gradient-like Method for Convex Constrained Nonlinear Monotone Equations and Signal Recovery,” Nonlinear Convex Anal. Optim., vol. 1, no. 1, pp. 1–23, 2022. 10.6028/jres.049.044M. R. Hestenes and E. Stiefel, "Methods of conjugate gradients for solving linear systems, "Journal of Research National Bureau Standard (1934), vol. 49, no. 6, pp. 409–436, Dec. 1952, doi: 10.6028/jres.049.044. 10.1080/10556788.2010.501379N. Andrei, “An accelerated conjugate gradient algorithm with guaranteed descent and conjugacy conditions for unconstrained optimization,” Optimization Methods and Software, vol. 27, no. 4–5, 2012, doi: 10.1080/10556788.2010.501379. 10.52866/ijcsm.2022.01.01.001M. M. Abed, U. Öztürk, and H. M. Khudhur, “Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations,” Iraqi J. Computer Science and Math., vol. 3, no. 1, pp. 1–10, Jan. 2022, doi: 10.52866/ijcsm.2022.01.01.001. Y. A. Laylani, B. A. Hassan, and H. M. Khudhur, “Enhanced spectral conjugate gradient methods for unconstrained optimization,” Computer Science, vol. 18, no. 2, pp. 163–172, 2023. N. Andrei, “Numerical comparison of conjugate gradient algorithms for unconstrained optimization,” Stud. Informatics Control, vol. 16, pp. 333–352, 2007. 10.11591/ijeecs.v22.i3.pp1643-1649H. N. Jabbar and B. A. Hassan, “Twoversions of descent conjugate gradient methods for large-scale unconstrained optimization,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 22, no. 3, p. 1643, Jun. 2021, doi: 10.11591/ijeecs.v22.i3.pp1643-1649. 10.11591/ijeecs.v28.i3.pp1510-1517Y. Ismail Ibrahim and H. Mohammed Khudhur, “Modified three-term conjugate gradient algorithm and its applications in image restoration,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 28, no. 3, pp. 1510–1517, Dec. 2022, doi: 10.11591/ijeecs.v28.i3.pp1510- 1517. I. A. R. Moghrabi, "A New Formulation for Quasi-Newton Methods," WSEAS Transactions on Mathematics, vol. 18, pp. 79-84, 2019, DOI: 10.1007/s00245-001-0003-0E. G. Birgin and J. M. Martínez, “A Spectral Conjugate Gradient Method for Unconstrained Optimization,” Appl. Math. Optim., vol. 43, no. 2, pp. 117–128, 2001, doi: 10.1007/s00245-001-0003-0. 10.29020/nybg.ejpam.v15i4.4575Y. Laylani, B. A. Hassan, and H. M. Khudhur, “A New Class of Optimization Methods Based on Coefficient Conjugate Gradient,” Eur. J. Pure Appl. Math., vol. 15, no. 4, pp. 1908–1916, 2022. 10.1007/s002450010019Y. H. Dai, “New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods,” Appl. Math. Optim., vol. 43, no. 1, pp. 87–101, Jan. 2001, doi: 10.1007/s002450010019. 10.1016/j.na.2010.09.046Z.-F. Dai, “Two modified HS type conjugate gradient methods for unconstrained optimization problems,” Nonlinear Anal. Theory, Methods Appl., vol. 74, no. 3, pp. 927–936, 2011. N. Andrei, “An Unconstrained Optimization Test Functions Collection,” Adv. Model. Optim., vol. 10, no. 1, pp. 147–161, 2008. 10.1007/s11075-021-01157-yZ. Aminifard and S. Babaie-Kafaki, “Dai– Liao extensions of a descent hybrid nonlinear conjugate gradient method with application in signal processing,” Numer. Algorithms, vol. 89, no. 3, pp. 1369–1387, Mar. 2022, doi: 10.1007/s11075-021-01157-y. 10.37394/23206.2021.20.78A. Olawale, I. Osinuga, R. Raji, "A Globally Convergent Hybrid FR-PRP Conjugate Gradient Method for Unconstrained Optimization Problems", WSEAS Transactions on Mathematics, vol. 20, pp. 736-744, 2021. 10.37394/232018.2021.9.17S. Singh, S. Gutta, A. Hadaegh, "Stock Prediction Using Machine Learning", WSEAS Transactions on Computer Research, vol. 9, pp. 152-158, 2021. 10.3934/math.2023001M. Malik, I. Mohammed Sulaiman, A. Bala Abubakar, G. Ardaneswari, S. Sukono. A new family of hybrid three-term conjugate gradient method for unconstrained optimization with application to image restoration and portfolio selection. AIMS Mathematics, 2023, 8(1):1-28. doi: 10.3934/math.2023001.