A family of parallel quasi-Newton algorithms for unconstrained minimization

[1] A.I. Ahmed, A new parameter free filled function for solving unconstrained global optimization problems, Int. J. Comput. Math. 98 (2021) 106–119.

[2] C.G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comput. 19 (1965) 577–593.

[3] R.H. Byrd, R.B. Schnabel and G.A. Shultz, Parallel quasi-Newton methods for solving the unconstrained optimization, Math. Prog. 42 (1988) 273–306.

[4] D. Chazan and W.L. Miranker, A nongradient and parallel algorithm for unconstrained minimization, SIAM J. Cont. 8 (1970) 207–217.

[5] J.J. E. Dennis and V. Torczon, Direct search methods in parallel machines, SIAM J. Opt. 1 (1991) 448–474.

[6] T.M. El–Gindy, M.S. Salim and A.I. Ahmed, A Modified partial quadratic interpolation method for unconstrained optimization, J. Conc. Appl. Math. 11 (2013) 136–146.

[7] T.M. El-Gindy, M.S. Salim and A.I. Ahmed, A new filled function method applied to unconstrained global optimization, Appl. Math. Comput. 273 (2016) 1246–1256.

[8] H. Fischer and K. Ritter, An asynchronous parallel Newton method, Math. Prog. 42 (1988) 363–374.

[9] M. Fukushima, Parallel variable transformation in unconstrained optimization, SIAM J. Opt. 8 (1998) 658–672.

[10] P.E. Gill, W. Murray and M. H. Wright, Practical optimization, Academic Press, London, 1981.

[11] L. Grandinetti, Factorization versus nonfactorization in quasi-Newtonian methods for differentiable optimization, Report N5, Dipartimento di Sistemi, Universita della Calabria 1978.

[12] H.Y. Huang, Unified approach to quadratically convergent algorithms for function minimization, J. Opt. Theo. Appl. 5 (1970) 405–423.

[13] J.K. Liu and S.J. Li, New three–term conjugate gradient method with guaranteed global convergence, Int. J. Comput. Math. 91 (2014) 1744–1754.

[14] F.A. Lootsma, Parallel Newton–Raphson methods for unconstrained minimization with asynchronous updates of the Hessian matrix or its inverse, M. Grauer, D.B. Pressmar (Eds.), Parallel computing and mathematical optimization, Springer-Verlag, Berlin, 1991, pp. 1-18.

[15] O.L. Mangasarian, Parallel gradient distribution in unconstrained optimization, SIAM J. Cont. Opt. 33 (1995) 1916–1925.

[16] J. Moreau, Proximite et dualite dans un espace hilbertien, Bull. Soc. Math. France 93 (1965) 273–299.

[17] J.J. More, B.S. Garbow and K.E. Hillstrome, Testing unconstrained optimization software, ACM Trans. Math. Soft. 7 (1981) 17–41.

[18] J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J. 7 (1965) 308–313.

[19] L.P. Pang and Z.Q. Xia, A PVT-TYPE algorithm for minimization a nonsmooth convex function, Serdica Math. J. 29 (2003) 11–32.

[20] K.D. Patel, Implementation of a parallel (SIMD) modified Newton method on the ICL DAP, Technical Report No. 131, Numerical Optimization Centre, The Hatfield Polytechnic (1982).

[21] P.K.-H. Phua, W. Fan, Y. Zeng, Parallel algorithms for large-scale nonlinear optimization, Int. Trans. Opl Res. 5 (1998) 67–77.

[22] M.J.D. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Comput. J. 7 (1964) 155–162.

[23] K. Ritter, Private communications in symposium on parallel optimization 3, July 1993.

[24] M.S. Salim and A.I. Ahmed, A piecewise polynomial approximation for solving nonlinear optimal control problems, Far East J. Appl. Math. 95 (2016) 195–213.

[25] M.S. Salim and A.I. Ahmed, A family of quasi-Newton methods for unconstrained optimization problems, Opt. 67 (2018) 1717–1727.

[26] M.S. Salim and A.I. Ahmed, A quasi-Newton augmented Lagrangian algorithm for constrained optimization problems, J. Intel. Fuzzy Syst. 35 (2018) 2373–2382.

[27] F. Sloboda, Parallel method of conjugate directions for minimization, Appl. Mat. 20 (1975) 436–446.

[28] F. Sloboda, A conjugate directions method and its applications, Proc. 8th IFIP Conf. Optim.  Tech., 1977.

[29] C. H. Still, Parallel quasi-Newton methods for unconstrained optimization, Proc. fifth Distrib. Memory Comput. Conf., 1990, April 8–12, 263-271.

[30] C.H. Still, The parallel BFGS Method for unconstrained minimization, Proc. Sixth Distrib. Memory Comput. Conf., 1991, April 28–May 1, pp. 347-354.

[31] T.A. Straeter, A parallel variable metric optimization algorithm, Technical report D-7329 NASA Langley Research center, Hampton, Va, 1973.

[32] C. Sutti, A new method for unconstrained minimization without derivatives, 277–289, In Towards global optimization, North Holland, 1978.

[33] C. Sutti, Nongradient minimization methods for parallel processing computers, Part 1, J. Opt. Theo. Appl. 39 (1983) 465-474.

[34] C. Sutti, Nongradient minimization methods for parallel processing computers, Part 2, J. Opt. Theo. Appl. 39 (1983) 475–488.

[35] A.J. Umbarkar, M.S. Joshi and W.-Ch. Hong, Multithreaded parallel dual population genetic algorithm (MPDPGA) for unconstrained function optimizations on a multi-core system, Appl. Math. Comput. 243 (2014) 936–949.

[36] P.J.M. van Laarhoven, Parallel variable matrix Algorithms for unconstrained optimization, Math. Prog. 33 (1985) 68-81.

[37] Y. Xiao, Z. Wei and Z. Wang, A limited memory BFGS–type method for large–scale unconstrained optimization, Comput. Math. Appl. 56(4) (2008) 1001–1009.

[38] K. Yosida, Functional analysis, Springer Verlag, Berlin, 1964.

[39] W.I. Zangwill, Minimizing a function without calculating derivatives, Comput. J. 10 (1967) 293–296.