References
- El-Gindy TM, Salim MS, Ahmed AI. A modifid partial quadratic interpolation method for unconstrained optimization. J Concr Appl Math. 2013;11:136–146.
- Salim MS, Ahmed AI. A piecewise polynomial approximation for solving nonlinear optimal control problems. Far East J Appl Math. 2016;95:195–213.
- Salim MS, Ahmed AI. A family of quasi–Newton methods for unconstrained optimization problems. Optimization. 2018;67:1717–1727.
- Salim MS, Ahmed AI. A quasi-Newton augmented Lagrangian algorithm for constrained optimization problems. J Intell Fuzzy Syst. 2018;35:2373–2382.
- Salim MS, Ahmed AI. A family of parallel quasi-Newton algorithms for unconstrained minimization. Int J Nonlinear Anal Appl. 2021;12:1123–1133.
- Dang CY, Ma W, Liang JY. A deterministic annealing algorithm for approximating a solution of the min-bisection problem. Neural Netw. 2009;22:58–66.
- Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by simulate annealing. Science. 1983;220:671–680.
- Holland JH. Genetic algorithms. Sci Am. 1992;4:14–50.
- Leung YW, Wang YP. Multiobjective programming using uniform design and genetic algorithm. IEEE Trans Syst Man Cybernet C. 2000;30:293–304.
- Bai L, Liang JY, Dang CY, et al. A cluster centers initialization method for clustering categorical data. Expert Syst Appl. 2012;39:8022–8029.
- Storn R, Price K. Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim. 1997;11:341–359.
- Parsopoulos KE, Vrahatis MN. On the computation of all global minimizers through particle swarm optimizzation. IEEE Trans Evol Comput. 2004;8:211–224.
- El-Gindy TM, Salim MS, Ahmed AI. A new filled function method applied to unconstrained global optimization. Appl Math Comput. 2016;273:1246–1256.
- Gao CL, Yang YJ, Han BS. A new class of filled functions with one parameter for global optimization. Comput Math Appl. 2011;62:2393–2403.
- Gao Y, Yang Y, You M. A new filled function method for global optimization. Appl Math Comput. 2015;268:685–695.
- Ge RP. A filled function method for finding a global minimizer of a function of several variables. Math Program. 1990;46:191–204.
- Ge RP, Qin YF. A class of filled functions for finding global minimizers of a function of several variables. J Optim Theory Appl. 1987;54:241–252.
- Liang YM, Zhang LS, Li MM, et al. A filled function method for global optimization. J Comput Appl Math. 2007;205:16–31.
- Lin H, Gao Y, Wang Y. A continuously differentiable filled function method for global optimization. Numer Algorithms. 2014;66:511–523.
- Lin H, Wang Y, Fan L. A filled function method with one parameter for unconstrained global optimization. Appl Math Comput. 2011;218:3776–3785.
- Lin H, Wang Y, Fan L, et al. A new discrete filled function method for finding global minimizer of the integer programming. Appl Math Comput. 2013;219:4371–4378.
- Lin H, Wang Y, Gao Y, et al. A filled function method for global optimization with inequality constraints. Comput Appl Math. 2018;37:1524–1536.
- Liu H, Wang Y, Guan S, et al. A new filled function method for unconstrained global optimization. Int J Comput Math. 2017;94:2283–2296.
- Liu X. Finding global minima with a computable filled function. J Global Optim. 2001;19:151–161.
- Liu X. A class of continuously differentiable filled functions for global optimization. IEEE Trans Syst Man Cybernet A. 2008;38:38–47.
- Liu X, Xu WS. A new filled function applied to global optimization. Comput Oper Res. 2004;31:61–80.
- Lucidi S, Piccialli V. New classes of globally convexized filled functions for global optimization. J Global Optim. 2002;24:219–236.
- Ma SZ, Yang YJ, Liu HQ. A parameter free filled function for unconstrained global optimization. Appl Math Comput. 2010;215:3610–3619.
- Shang Y-L, Pu D-G, Jiang A-P. Finding global minimizer with one-parameter filled function on unconstrained global optimization. Appl Math Comput. 2007;191:176–182.
- Shang Y-L, Zhang L-S. Finding discrete global minima with a filled function for integer programming. Eur J Oper Res. 2008;189:31–40.
- Wang C, Yang Y, Li J. A new filled function method for unconstrained global optimization. J Comput Appl Math. 2009;225:68–79.
- Wang W, Shang Y, Zhang L. A filled function method with one parameter for box constrained global optimization. Appl Math Comput. 2007;194:54–66.
- Wang XL, Zhou GB. A new filled function for unconstrained global optimization. Appl Math Comput. 2006;174:419–429.
- Wang Y-J, Zhang J-S. A new constructing auxiliary function method for global optimization. Math Comput Model. 2008;47:1396–1410.
- Wei F, Wang Y, Lin H. A new filled function method with two parameters for global optimization. J Optim Theory Appl. 2014;163:510–527.
- Yang Y, Gao Y. A new filled function method for global optimization. In: IEEE International Conference on Digital Signal Processing; Singapore; 2015. p. 54–58.
- Yang YJ, Shang YL. A new filled function method for unconstrained global optimization. Appl Math Comput. 2006;173:501–512.
- Zhang L-S, Ng C-K, Li D, et al. A new filled function method for global optimization. J Global Optim. 2004;28:17–43.
- Zhu WX. Dynamic globally concavized filled function method for continuous global optimization. J Optim Theory Appl. 2008;139:635–648.
- Cetin BC, Barhen J, Burdick JW. Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization. J Optim Theory Appl. 1993;77:97–126.
- Xu Y-T, Zhang Y, Wang S-G. A modified tunneling function method for non-smooth global optimization and its application in artificial neural network. Appl Math Model. 2015;39:6438–6450.
- Yao Y. Dynamic tunneling algorithm for global optimization. IEEE Trans Syst Man Cybernet. 1989;19:1222–1230.
- Mladineo RH. An algorithm for finding the global maximum of a multimodal, multivariate function. Math Program. 1986;34:188–200.
- Zhu WX. Unsolvability of some optimization problems. Appl Math Comput. 2006;174:921–926.
- Ahmed AI. A new parameter free filled function for solving unconstrained global optimization problems. Int J Comput Math. 2021;98:106–119.
- Toint PhL. Numerical solution of large sets of algebraic nonlinear equations. Math Comput. 1986;46:175–189.
- Yuan G, Lu X. A new backtracking inexact BFGS method for symmetric nonlinear equations. Comput Math Appl. 2008;55:116–129.
- Yuan G, Yao S. A BFGS algorithm for solving symmetric nonlinear equations. Optimization. 2013;62:82–95.
- Yuan G, Lu X, Wei Z. BFGS trust-region method for symmetric nonlinear equations. J Comput Appl Math. 2009;230:44–58.
- Yuan G, Wei Z, Lu X. A BFGS trust-region method for nonlinear equations. Computing. 2011;92:317–333.
- Yuan G, Meng Z, Li Y. A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations. J Optim Theory Appl. 2016;168:129–152.
- Fasano G, Lampariello F, Sciandrone M. A truncated nonmonotone Gauss-Newton method for large-scale nonlinear least-squares problems. Comput Optim Appl. 2006;34:343–358.
- Li D, Qi L, Zhou S. Descent directions of quasi-Newton methods for symmetric nonlinear equations. SIAM J Numer Anal. 2002;40:1763–1774.
- Ahmad F, Tohidi E, Carrasco JA. A parameterized multi-step Newton method for solving systems of nonlinear equations. Numer Algorithms. 2015;71:631–653.
- Ullah MZ, Serra-Capizzano S, Ahmad F, et al. A higher order multi-step iterative method for computing the numerical solution of systems of nonlinear equations associated with nonlinear PDEs and ODEs. J Comput Anal Appl. 2016;269:972–987.
- Lin Y, Yang Y, Mammadov M. A new filled function method for nonlinear equations. Appl Math Comput. 2009;210:411–421.
- Wang C, Luo R, Wu K, et al. A new filled function method for an unconstrained nonlinear equation. J Comput Appl Math. 2011;235:1689–1699.
- Wu ZY, Mammadov M, Bai FS, et al. A filled function method for nonlinear equations. Appl Math Comput. 2007;189:1196–1204.
- Sahiner A, Yilmaz N, Kapusuz G. A novel modeling and smoothing technique in global optimization. J Ind Manag Optim. 2019;15:113–130.