Audet C, Dennis J J E. Analysis of generalized pattern searches[J]. SIAMJournal on Optimization, 2003, 13: 889-903.
[2]
Audet C, Dennis J J E. Mesh adaptive direct search algorithms for constrained optimization[J]. SIAM Journal on Optimization, 2006, 17: 188-217.
[3]
Conn A R, Scheinberg K, Vicent L N. Introduction to derivative-free optimization. Philadelphia: SIAM-MPS, 2009.
[4]
Coope I D, Price C J. Frame based methods for unconstrained optimization[J]. Journal of Opti- mization Theory and Application, 2000, 107: 261-274.
[5]
Coope I D, Price C J. On the convergence of grid-based methods for unconstrained optimization[J]. SIAM Journal on Optimizatioin, 2001, 11: 859-869.
[6]
Coope I D, Price C J. Positive bases in numerical optimization[J]. Computational Optimization and Applications, 2002, 21 (2): 169-176.
[7]
Hooke R, Jeeves T A. Direct search solution of numerical and statistical problems[J]. Journal of the ACM, 1961, 8: 212-229.
[8]
Kolda T G, Lewis R M, Torczon V. Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods. SIAM Review, 2003, 45: 385-482.
[9]
Lewis R M, Torczon V, Trosset M W. Why pattern search works. Optima, 1998, 59: 1-7.
[10]
Lewis R M, Torczon V, Trosset M W. Direct search methods: Then and now[J]. Journal of Computational and Applied Mathematics, 2000, 124: 191-207.
[11]
Price C J, Coope I D. Frames and grids in unconstrained and linearly constrained optimization: a nonsmooth approach[J]. SIAM Journal on Optimization, 2003, 14 (2): 415-438.
[12]
Torczon V. On the convergence of pattern search algorithms[J]. SIAM Journal on Optimization, 1997, 7: 1-25.
[13]
Trosset M W. I know it when I see it: Toward a definition of direct search methods[J]. SIAG/OPT Views-and-News: A Forum for the SIAM Activity Group on Optimization, 1997, 9: 7-10.
[14]
Liu Q F. Linear scaling and the DIRECT algorithm[J]. Journal of Global Optimization, 2013, 56 (3): 1233-1245.
[15]
Liu Q F, Zeng J P. Global optimization by multilevel partition[J]. Journal of Global Optimization, 2015, 61 (1): 47-69.
[16]
Liu Q F, Zeng J P, Yang G. MrDIRECT: A multilevel robust DIRECT algorithm for global optimization problems. Journal of Global Optimization, DOI: 10.1007/s10898-014-0241-8, online, 2014.
[17]
Davidon W C. Variable metric method for minimization[J]. SIAM Journal on Optimization, 1992, 1: 1-17.
[18]
Rosenbrock H H. An automatic method for finding the greatest or least value of a function[J]. Computer Journal, 1960, 3: 175-184.
[19]
Torczon V. On the convergence of the multidirectional search algorithm[J]. SIAM Journal on Optimization, 1991, 1: 123-145.
[20]
Lewis R M, Torczon V. Rank ordering and positive bases in pattern search algorithms. Tech. Report 96-71, Institute for Computer Applications in Science and Engineering, NASA Langley Rearch Center, Hampson, VA, 1996.
[21]
Audet C. Convergence results for pattern search algorithms are tight[J]. Optimization and Engi- neering, 2004, 5(2): 101-122.
[22]
Coope I D, Price C J. A direct search frame-based conjugate gradients method[J]. Journal of Computational Mathematics, 2004, 22: 489-500.
[23]
Custódio A L, Vicente L N. Using sampling and simplex derivatives in pattern search methods[J]. SIAM Journal on Optimization, 2007, 18: 537-555.
[24]
Custódio A L, Dennis J E, Vicente L N. Using simplex gradients of nonsmooth functions in direct search methods[J]. IMA Journal of Numerical Analysis, 2008, 28 (4): 770-784.
[25]
Custódio A L, Rocha H, Vicente L N. Incorporating minimum Frobenius norm models in direct search[J]. Computational Optimization and Applications, 2010, 46: 265-278.
[26]
Sandia National Laboratories. APPSPACK: Asynchronous Pattern Search, 5.0.1 edition, February 2007. https://software.sandia.gov/appspack/.
[27]
Davis C. Theory of positive linear dependence[J]. American Journal of Mathematics, 1954, 76: 733-746.
[28]
Regis R G. On the properties of positive spanning sets and positive bases. Optimization and Engineering, 2015.
[29]
Zhang L, Zou W J, Li D H. A descent modified Polad-Ribiere-Polyak conjugate gradient method and its global convergence[J]. IMA Journal of Numerical Analysis, 2006, 26: 629-640.
[30]
Liu Q F. Two minimal positive bases based direct search conjugate gradient methods for compu- tationally expensive functions[J]. Numerical Algorithms, 2011, 58(4): 461-474.
[31]
Moré J J, Garbow B S, Hillstrom K E. Testing unconstrained optimization software[J]. ACM Transactions on Mathematical Software, 1981, 7(1): 17-41.
[32]
CUTEr: A constrained and unconstrained testing enviroment, Revisited. Website. http://cuter.rl.ac.uk/cuter-www/
[33]
Moré J J, Wild S M. Benchmarking derivative-free optimization algorithms[J]. SIAM Journal on Optimization, 2009, 20: 172-191.
[34]
Dolan E D, Moré J J. Benchmarking optimization software with performance profiles[J]. Mathe- matical Programming, 2002, 91: 201-213.