A comparison of Quasi-Newton methods considering line search conditions in unconstrained minimization

References

• N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim 10 (2008), pp. 147–161.
   Google Scholar
• R.H. Byrd, J. Nocedal, and Y.X. Yuan, Global convergence of a cass of quasi-newton methods on convex problems, SIAM Journal on Numerical Analysis 24 (1987), pp. 1171–1190. doi: 10.1137/0724077
   Web of Science ®Google Scholar
• E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Mathematical programming 91 (2002), pp. 201–213. doi: 10.1007/s101070100263
   Web of Science ®Google Scholar
• V. Ganguly and T.L. Schmitz, Spindle dynamics identification using particle swarm optimization, Journal of Manufacturing Processes 15 (2013), pp. 444–451. doi: 10.1016/j.jmapro.2013.05.008
   Web of Science ®Google Scholar
• I. Griva, S.G. Nash, and A. Sofer, Linear and nonlinear optimization, Vol. 108, Siam, 2009.
   Google Scholar
• B.A. Hassan and M.A. Kahya, A new class of quasi-newton updating formulas for unconstrained optimization, Journal of Interdisciplinary Mathematics 24 (2021), pp. 2355–2366. doi: 10.1080/09720502.2021.1961980
   Web of Science ®Google Scholar
• M. Jamil and X.S. Yang, A literature survey of benchmark functions for global optimisation problems, International Journal of Mathematical Modelling and Numerical Optimisation 4 (2013), pp. 150–194. doi: 10.1504/IJMMNO.2013.055204
   Google Scholar
• K. Kiran, Initial parameters estimation for euler-bernoulli beam fitting of measured frequency response functions, CIRP Journal of Manufacturing Science and Technology 38 (2022), pp. 62–72. doi: 10.1016/j.cirpj.2022.04.007
   Web of Science ®Google Scholar
• K. Kiran, Performance evaluation of a conjugate gradient method considering step length computation techniques in geometry fitting of coordinate measuring machine data, Measurement 196 (2022), p. 111202. doi: 10.1016/j.measurement.2022.111202
   Web of Science ®Google Scholar
• K. Kiran, M. Rubeo, M.C. Kayacan, and T. Schmitz, Two degree of freedom frequency domain surface location error prediction, Precision Engineering 48 (2017), pp. 234–242. doi: 10.1016/j.precisioneng.2016.12.006
   Web of Science ®Google Scholar
• A. Kroll and H. Schulte, Benchmark problems for nonlinear system identification and control using soft computing methods: Need and overview, Applied Soft Computing 25 (2014), pp. 496–513. doi: 10.1016/j.asoc.2014.08.034
   Web of Science ®Google Scholar
• D.H. Li and M. Fukushima, A derivative-free line search and global convergence of broyden-like method for nonlinear equations, Optimization Methods and Software 13 (2000), pp. 181–201. doi: 10.1080/10556780008805782
   Web of Science ®Google Scholar
• D.H. Li and M. Fukushima, A modified bfgs method and its global convergence in nonconvex minimization, Journal of Computational and Applied Mathematics 129 (2001), pp. 15–35. doi: 10.1016/S0377-0427(00)00540-9
   Web of Science ®Google Scholar
• D.H. Li and M. Fukushima, On the global convergence of the bfgs method for nonconvex unconstrained optimization problems, SIAM Journal on Optimization 11 (2001), pp. 1054–1064. doi: 10.1137/S1052623499354242
   Web of Science ®Google Scholar
• D. Li and M. Fukushima, A globally and superlinearly convergent gauss-newton-based bfgs method for symmetric nonlinear equations, SIAM Journal on numerical Analysis 37 (1999), pp. 152–172. doi: 10.1137/S0036142998335704
   Web of Science ®Google Scholar
• H. Liu, B. Xu, D. Lu, and G. Zhang, A path planning approach for crowd evacuation in buildings based on improved artificial bee colony algorithm, Applied Soft Computing 68 (2018), pp. 360–376. doi: 10.1016/j.asoc.2018.04.015
   Web of Science ®Google Scholar
• J.M. Martinez, Practical quasi-newton methods for solving nonlinear systems, Journal of Computational and Applied Mathematics 124 (2000), pp. 97–121. doi: 10.1016/S0377-0427(00)00434-9
   Web of Science ®Google Scholar
• I.R. Meneghini, M.A. Alves, A. Gaspar-Cunha, and F.G. Guimaraes, Scalable and customizable benchmark problems for many-objective optimization, Applied Soft Computing 90 (2020), p. 106139. doi: 10.1016/j.asoc.2020.106139
   Web of Science ®Google Scholar
• J.J. Moré and S.M. Wild, Benchmarking derivative-free optimization algorithms, SIAM Journal on Optimization 20 (2009), pp. 172–191. doi: 10.1137/080724083
   Web of Science ®Google Scholar
• J. Nocedal and S. Wright, Numerical optimization, Springer Science & Business Media, 2006.
   Google Scholar
• F. Raeesi, B.F. Azar, H. Veladi, and S. Talatahari, An inverse tsk model of mr damper for vibration control of nonlinear structures using an improved grasshopper optimization algorithm, Structures 26 (2020), pp. 406–416. doi: 10.1016/j.istruc.2020.04.026
   Web of Science ®Google Scholar
• P.K. Salonga, J.M. Inaudito, and R. Mendoza, An unconstrained minimization technique using successive implementations of Golden Search algorithm, in AIP Conference Proceedings, Vol. 2192, 060018. AIP Publishing LLC, 2019, pp. 1–20.
   Google Scholar
• A. Tangherloni, S. Spolaor, P. Cazzaniga, D. Besozzi, L. Rundo, G. Mauri, and M.S. Nobile, Biochemical parameter estimation vs. benchmark functions: A comparative study of optimization performance and representation design, Applied Soft Computing 81 (2019), p. 105494. doi: 10.1016/j.asoc.2019.105494
   Web of Science ®Google Scholar
• C. Xu and J. Zhang, A survey of quasi-newton equations and quasi-newton methods for optimization, Annals of Operations research 103 (2001), pp. 213–234. doi: 10.1023/A:1012959223138
   Web of Science ®Google Scholar
• G. Yuan, Z. Sheng, B. Wang, W. Hu, and C. Li, The global convergence of a modified bfgs method for nonconvex functions, Journal of Computational and Applied Mathematics 327 (2018), pp. 274–294. doi: 10.1016/j.cam.2017.05.030
   Web of Science ®Google Scholar
• G. Yuan and Z. Wei, Convergence analysis of a modified bfgs method on convex minimizations, Computational optimization and applications 47 (2010), pp. 237–255. doi: 10.1007/s10589-008-9219-0
   Web of Science ®Google Scholar
• G. Yuan, Z. Wei, and X. Lu, Global convergence of bfgs and prp methods under a modified weak wolfe-powell line search, Applied Mathematical Modelling 47 (2017), pp. 811–825. doi: 10.1016/j.apm.2017.02.008
   Web of Science ®Google Scholar
• J. Zhang and C. Xu, Properties and numerical performance of quasi-newton methods with modified quasi-newton equations, Journal of Computational and Applied Mathematics 137 (2001), pp. 269–278. doi: 10.1016/S0377-0427(00)00713-5
   Web of Science ®Google Scholar
• W. Zhou, A modified bfgs type quasi-newton method with line search for symmetric nonlinear equations problems, Journal of Computational and Applied Mathematics 367 (2020), p. 112454. doi: 10.1016/j.cam.2019.112454
   Web of Science ®Google Scholar
• W. Zhou and L. Zhang, Global convergence of the nonmonotone mbfgs method for nonconvex unconstrained minimization, Journal of computational and applied mathematics 223 (2009), pp. 40–47. doi: 10.1016/j.cam.2007.12.011
   Web of Science ®Google Scholar