Abstract
In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear convergence rate of the scheme is also proved in the vicinity of the solution. The advantages of the proposed scheme over the traditional schemes are justified with numerical table and graphical illustrations.
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References
Andrei, N.: An unconstrained optimization test functions collection. Adv. Model. Optim 10(1), 147–161 (2008)
Babajee, D., Dauhoo, M.: An analysis of the properties of the variants of Newtons method with third order convergence. Appl. Math. Comput. 183(1), 659–684 (2006)
Biglari, F., Ebadian, A.: Limited memory BFGS method based on a high-order tensor model. Comput. Optim. Appl. 60(2), 413–422 (2015)
Chakraborty, S.K., Panda, G.: A higher order iterative algorithm for multivariate optimization problem. J. Appl. Math. Inform. 32(5–6), 747–760 (2014)
Chakraborty, S.K., Panda, G.: Two-phase-SQP method with higher-order convergence property. J. Oper. Res. Soc. China 4(5), 385–396 (2016)
Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Programm. 91(2), 201–213 (2002)
Jensen, T.L., Diehl, M.: An approach for analyzing the global rate of convergence of quasi-Newton and truncated-Newton methods. J. Optim. Theory Appl. 1, 206–221 (2016)
Kanwar, V., Kumar, S., Kansal, M., Garg, A.: Efficient families of Newtons method and its variants suitable for non-convergent cases. Afrika Matematika 27(5–6), 767–779 (2016)
Nocedal, J., Wright, S.J.: Numerical Optimization, Springer Series in Operations Research and Financial Engineering, 2nd edn. Springer, New York (2006)
Sharma, J.R., Guha, R.K., Sharma, R.: An efficient fourth order weighted-Newton method for systems of nonlinear equations. Numer. Algorithm. 62(2), 307–323 (2013)
Soleymani, F., Lotfi, T., Bakhtiari, P.: A multi-step class of iterative methods for nonlinear systems. Optim. Lett. 8(3), 1001–1015 (2014)
Tapia, R.: On averaging and representation properties of the BFGS and related secant updates. Math. Programm. 153(2), 363–380 (2015)
Xiao, Y.H., Li, T.F., Wei, Z.X.: Global convergence of a modified limited memory BFGS method for non-convex minimization. Acta Math. Appl. Sin. Engl. Ser 29(3), 555–566 (2013)
Zhang, H., Ni, Q.: A new regularized quasi-Newton method for unconstrained optimization. Optim. Lett. 12(7), 1639–1658 (2018)
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Chakraborty, S.K., Panda, G. Two-phase quasi-Newton method for unconstrained optimization problem. Afr. Mat. 30, 737–746 (2019). https://doi.org/10.1007/s13370-019-00680-5
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DOI: https://doi.org/10.1007/s13370-019-00680-5