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Abubakar, A. B., Kumam, P., & Mohammad, H. (2020). A note on the spectral gradient projection method for nonlinear monotone equations with applications. Computational and Applied Mathematics, 39(2), 1-35. https://doi.org/10.1007/s40314-020-01151-5
Andrei, N. (2008). An unconstrained optimization test functions collection. Advanced Modeling and Optimization, 10(1), 147-161.
Antonelli, L., De Simone, V., & Di Serafino, D. (2016). On the application of the spectral projected gradient method in image segmentation. Journal of Mathematical Imaging and Vision, 54(1), 106-116. https://doi.org/10.1007/s10851-015-0591-y
Barzilai, J., & Borwein, J. M. (1988). Two-point step size gradient methods. IMA Journal of Numerical Analysis, 8(1), 141-148. https://doi.org/10.1093/imanum/8.1.141
Biglari, F., & Solimanpur, M. (2013). Scaling on the spectral gradient method. Journal of Optimization Theory and Applications, 158(2), 626-635. https://doi.org/10.1007/s10957-012-0265-5
Broyden, C. G. (1965). A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation, 19(92), 577-593.
Buzzi-Ferraris, G., & Manenti, F. (2013). Nonlinear systems and optimization for the chemical engineer: Solving numerical problems. John Wiley & Sons.
Byrd, R. H., & Nocedal, J. (1989). A tool for the analysis of quasi-Newton methods with application to unconstrained minimization. SIAM Journal of Numerical Analysis, 26, 727-739. https://doi.org/10.1137/0726042
Cauchy, A. (1847). Méthode générale pour la résolution des systemes d’équations simultanées [General method for solving systems of simultaneous equations]. Comptes rendus de l’Académie des Sciences, 25(1847), 536-538.
Chen, X., Liu, Y., Zhou, W., & Peng, X. (2017). Simplex-fruit fly optimization algorithm for solving systems of non-linear equations. In 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD) (pp. 615-620). IEEE Publishing. https://doi.org/10.1109/FSKD.2017.8393341
Cheng, W. Y., & Li, D. H. (2010). Spectral scaling BFGS method. Journal of Optimization Theory and Applications, 146(2), 305-319. https://doi.org/10.1007/s10957-010-9652-y
Cruz, W. L., & Raydan, M. (2003). Nonmonotone spectral methods for large-scale nonlinear systems. Optimization Methods and Software, 18(5), 583-599. https://doi.org/10.1080/10556780310001610493
Dai, Y. H., Hager, W. W., Schittkowski, K., & Zhang, H. (2006). The cyclic Barzilai-Borwein method for unconstrained optimization. IMA Journal of Numerical Analysis, 26(3), 604-627. https://doi.org/10.1093/imanum/drl006
De Asmundis, R., di Serafino, D., Riccio, F., & Toraldo, G. (2013). On spectral properties of steepest descent methods. IMA Journal of Numerical Analysis, 33(4), 1416-1435. https://doi.org/10.1093/imanum/drs056
Dolan, E. D., & Moré, J. J. (2002). Benchmarking optimization software with performance profiles. Mathematical Programming, 91(2), 201-213. https://doi.org/10.1007/s101070100263
Fang, X., Ni, Q., & Zeng, M. (2018). A modified quasi-Newton method for nonlinear equations. Journal of Computational and Applied Mathematics, 328, 44-58. https://doi.org/10.1016/j.cam.2017.06.024
Grosan, C., & Abraham, A. (2008). A new approach for solving nonlinear equations systems. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 38(3), 698-714. https://doi.org/10.1109/TSMCA.2008.918599
Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards, 49(6), 409-436.
Ibrahim, S. M., Yakubu, U. A., & Mamat, M. (2020). Application of spectral conjugate gradient methods for solving unconstrained optimization problems. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 10(2), 198-205. https://doi.org/10.11121/ijocta.01.2020.00859
Luenberger, D. G., & Ye, Y. (1984). Linear and nonlinear programming (Vol. 2). Addison-Wesley.
Marini, F. (2009). Neural networks. In R. Tauler & B. Walczak (Eds.), Comprehensive Chemometrics: Chemical and Biochemical Data Analysis (pp. 477-505). Elsevier. https://doi.org/10.1016/B978-044452701-1.00128-9
Martinez, J. M. (2000). Practical quasi-Newton methods for solving nonlinear systems. Journal of Computational and Applied Mathematics, 124(1-2), 97-121. https://doi.org/10.1016/S0377-0427(00)00434-9
Raydan, M. (1993). On the Barzilai and Borwein choice of steplength for the gradient method. IMA Journal of Numerical Analysis, 13(3), 321-326. https://doi.org/10.1093/imanum/13.3.321
Raydan, M. (1997). The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM Journal on Optimization, 7(1), 26-33. https://doi.org/10.1137/S1052623494266365
Raydan, M., & Svaiter, B. F. (2002). Relaxed steepest descent and Cauchy-Barzilai-Borwein method. Computational Optimization and Applications, 21(2), 155-167. https://doi.org/10.1023/A:1013708715892
Sim, H. S., Leong, W. J., & Chen, C. Y. (2019). Gradient method with multiple damping for large-scale unconstrained optimization. Optimization Letters, 13(3), 617-632. https://doi.org/10.1007/s11590-018-1247-9
Simpson, T. (1740). Essays on several curious and useful subjects, in speculative and mix’d mathematics. London, 1740, Article 81.
Solodov, M. V., & Svaiter, B. F. (1998). A globally convergent inexact Newton method for systems of monotone equations. In Reformulation: Nonsmooth, piecewise smooth, semismooth and smoothing methods (pp. 355-369). Springer. https://doi.org/10.1007/978-1-4757-6388-1_18
Turgut, O. E., Turgut, M. S., & Coban, M. T. (2014). Chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations. Computers & Mathematics with Applications, 68(4), 508-530. https://doi.org/10.1016/j.camwa.2014.06.013
Wallis, J. (1095). A treatise of algebra, both historical and practical. Philosophical Transactions of the Royal Society of London, 15(173), 1095-1106. https://doi.org/10.3931/e-rara-8842
Xiao, Y., Wang, Q., & Wang, D. (2010). Notes on the Dai–Yuan–Yuan modified spectral gradient method. Journal of Computational and Applied Mathematics, 234(10), 2986-2992. https://doi.org/10.1016/j.cam.2010.04.012
Yuan, G., & Lu, X. (2008). A new backtracking inexact BFGS method for symmetric nonlinear equations. Computers & Mathematics with Applications, 55(1), 116-129. https://doi.org/10.1016/j.camwa.2006.12.081
Zhang, L., & Zhou, W. (2006). Spectral gradient projection method for solving nonlinear monotone equations. Journal of Computational and Applied Mathematics, 196(2), 478-484. https://doi.org/10.1016/j.cam.2005.10.002
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e-ISSN 2231-8542