A non-monotone pattern search approach for systems of nonlinear equations

References

• M. Ahookhosh and K. Amini, An efficient nonmonotone trust-region method for unconstrained optimization, Numer. Algorithms 59 (2012), pp. 523–540. doi: 10.1007/s11075-011-9502-5
   Web of Science ®Google Scholar
• M. Ahookhosh, K. Amini, and M. Kimiaei, A globally convergent trust-region method for large-scale symmetric nonlinear systems, Numer. Funct. Anal. Optim. 36 (2015), pp. 830–855. doi: 10.1080/01630563.2015.1046080
   Web of Science ®Google Scholar
• M. Ahookhosh, H. Esmaeili, and M. Kimiaei, An effective trust-region-based approach for symmetric nonlinear systems, Int. J. Comput. Math. 90(3) (2013), pp. 671–690. doi: 10.1080/00207160.2012.736617
   Google Scholar
• G.E.P. Box, Evolutionary operation: A method for increasing industrial productivity, Appl. Stat. 6 (1957), pp. 81–101. doi: 10.2307/2985505
   Web of Science ®Google Scholar
• Y.H. Dai, On the nonmonotone line search, J. Optim. Theory Appl. 112(2) (2002), pp. 315–330. doi: 10.1023/A:1013653923062
   Web of Science ®Google Scholar
• E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201–213. doi: 10.1007/s101070100263
   Web of Science ®Google Scholar
• H. Esmaeili and M. Kimiaei, An improved adaptive trust-region method for unconstrained optimization, Math. Model. Anal. 19 (2014), pp. 469–490. doi: 10.3846/13926292.2014.956237
   Web of Science ®Google Scholar
• H. Esmaeili and M. Kimiaei, An efficient adaptive trust-region method for systems of nonlinear equations, Int. J. Comput. Math. 92 (2015), pp. 151–166. doi: 10.1080/00207160.2014.887701
   Web of Science ®Google Scholar
• H. Esmaeili and M. Kimiaei, A trust-region method with improved adaptive radius for systems of nonlinear equations, Math. Methods Oper. Res. 83(1) (2016), pp. 109–125. doi: 10.1007/s00186-015-0522-0
   Web of Science ®Google Scholar
• J.Y. Fan, Convergence rate of the trust region method for nonlinear equations under local error bound condition, Comput. Optim. Appl. 34 (2005), pp. 215–227. doi: 10.1007/s10589-005-3078-8
   Web of Science ®Google Scholar
• J. Fan and J. Pan, An improved trust region algorithm for nonlinear equations, Comput. Optim. Appl. 48(1) (2011), pp. 59–70. doi: 10.1007/s10589-009-9236-7
   Web of Science ®Google Scholar
• M.G. Gasparo, A nonmonotone hybrid method for nonlinear systems, Optim. Methods Softw. 13 (2000), pp. 79–94. doi: 10.1080/10556780008805776
   Web of Science ®Google Scholar
• M.G. Gasparo, A. Papini, and A. Pasquali, Nonmonotone algorithms for pattern search methods, Numer. Algorithms 28 (2001), pp. 171–186. doi: 10.1023/A:1014046817188
   Web of Science ®Google Scholar
• L. Grippo, F. Lampariello, and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal. 23 (1986), pp. 707–716. doi: 10.1137/0723046
   Web of Science ®Google Scholar
• L. Grippo, F. Lampariello, and S. Lucidi, A truncated Newton method with nonmonotone line search for unconstrained optimization, J. Optim. Theory Appl. 60(3) (1989), pp. 401–419. doi: 10.1007/BF00940345
   Web of Science ®Google Scholar
• L. Grippo, F. Lampariello, and S. Lucidi, A class of nonmonotone stabilization methods in unconstrained optimization, Numer. Math. 59 (1991), pp. 779–805. doi: 10.1007/BF01385810
   Web of Science ®Google Scholar
• R. Hooke and T.A Jeeves, Direct search solution of numerical and statistical problems, J. ACM 8 (1961), pp. 212–229. doi: 10.1145/321062.321069
   Google Scholar
• W. LaCruz, C. Venezuela, J.M. Martínez, and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems of equations: Theory and experiments, Technical Report RT–04–08, July 2004.
   Google Scholar
• R.M Lewis and V. Torczon, Pattern search algorithms for bound constrained minimization, SIAM. J. Optim. 9 (1999), pp. 1082–1099. doi: 10.1137/S1052623496300507
   Web of Science ®Google Scholar
• R.M. Lewis and V. Torczon, Pattern search methods for linearly constrained minimization, SIAM. J. Optim. 10 (2000), pp. 917–941. doi: 10.1137/S1052623497331373
   Web of Science ®Google Scholar
• R.M. Lewis, V. Torczon, and M.W. Trosset, Why pattern search works, Optima (1988), pp. 1–7.
   Google Scholar
• R.M. Lewis, V. Torczon, and M.W. Trosset, Direct search methods: Then and now, J. Comput. Appl. Math. 124 (2000), pp. 191–207. doi: 10.1016/S0377-0427(00)00423-4
   Web of Science ®Google Scholar
• S. Lucidi and M. Sciandrone, On the global convergence of derivative free methods for unconstrained optimization, Technical Report 32–96, DIS, Universita' di Roma ‘La Sapienza’, 1996.
   Google Scholar
• L. Lukšan and J. Vlček, Sparse and partially separable test problems for unconstrained and equality constrained optimization, Techical Report, No. 767, January 1999.
   Google Scholar
• J.J. Moré, B.S. Garbow, and K.E. Hillström, Testing Unconstrained Optimization Software, ACM Trans. Math. Softw. 7 (1981), pp. 17–41. doi: 10.1145/355934.355936
   Web of Science ®Google Scholar
• J. Nocedal and J.S. Wright, Numerical Optimization, Springer, NewYork, 2006.
   Google Scholar
• Z.J. Shi and S. Wang, Modified nonmonotone Armijo line search for descent method, Numer. Algorithms 57(1) (2011), pp. 1–25. doi: 10.1007/s11075-010-9408-7
   Web of Science ®Google Scholar
• P.L. Toint, An assessment of nonmonotone linesearch techniques for unconstrained optimization, SIAM J. Sci. Comput. 17 (1996), pp. 725–739. doi: 10.1137/S106482759427021X
   Web of Science ®Google Scholar
• V. Torczon, Multidirectional search: A direct search algorithm for parallel machines, Ph.D. thesis, Rice University, Houston, TX, 1989.
   Google Scholar
• V. Torczon, On the convergence of the multidirectional search algorithm, SIAM J. Optim. 1 (1991), pp. 123–145. doi: 10.1137/0801010
   Web of Science ®Google Scholar
• V. Torczon, On the convergence of pattern search algorithms, SIAM J. Optim. 7 (1997), pp. 1–25. doi: 10.1137/S1052623493250780
   Web of Science ®Google Scholar
• G.L. Yuan and X.W. Lu, A new backtracking inexact BFGS method for symmetric nonlinear equations, Comput. Math. Appl. 55 (2008), pp. 116–129. doi: 10.1016/j.camwa.2006.12.081
   Web of Science ®Google Scholar
• G.L. Yuan and M.J. Zhang, A three-terms Polak-R*ibière-Polyak conjugate gradient algorithm for large-scale nonlinear equations, J. Comput. Appl. Math. 286 (2015), pp. 186–195. doi: 10.1016/j.cam.2015.03.014
   Web of Science ®Google Scholar
• G.L. Yuan, S. Lu, and Z. Wei, A new trust-region method with line search for solving symmetric nonlinear equations, Int. J. Comput. Math. 88(10) (2011), pp. 2109–2123. doi: 10.1080/00207160.2010.526206
   Web of Science ®Google Scholar
• G.L. Yuan, Z.H. Meng, and Y. Li, A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations, J. Optim. Theory Appl. 168 (2016), pp. 129–152. doi: 10.1007/s10957-015-0781-1
   Web of Science ®Google Scholar
• G.L. Yuan, X.W. Lu, and Z.X. Wei, BFGS trust-region method for symmetric nonlinear equations, J. Comput. Appl. Math. 230 (2009), pp. 44–58. doi: 10.1016/j.cam.2008.10.062
   Web of Science ®Google Scholar
• G.L. Yuan, Z.X. Wei, and X.W. Lu, A BFGS trust-region method for nonlinear equations, Computing 92(4) (2011), pp. 317–333. doi: 10.1007/s00607-011-0146-z
   Web of Science ®Google Scholar
• H.C Zhang and W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14(4) (2004), pp. 1043–1056. doi: 10.1137/S1052623403428208
   Web of Science ®Google Scholar
• J. Zhang and Y. Wang, A new trust region method for nonlinear equations, Math. Methods Oper. Res. 58 (2003), pp. 283–298. doi: 10.1007/s001860300302
   Web of Science ®Google Scholar