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A nonconvergent example for the iterative waterfilling algorithm
A derivativefree trustregion algorithm for unconstrained optimization with controlled error
1.  Graduate School of Informatics, Kyoto University, Yoshidahonmachi, Sakyoku, Kyoto, 6068501,, Japan 
2.  Graduate School of Informatics, Kyoto University, Yoshidahonmachi, Sakyoku, Kyoto, 6068501 
References:
[1] 
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and unconstrained testing environment,, ACM Transactions on Mathematical Software, 21 (1995), 123. doi: 10.1145/200979.201043. 
[2] 
A. J. Booker, J. E. Dennis, P. D. Frank, D. B. Serafini, V. Torczon and M. W. Trosset, A rigorous framework for optimization of expensive functions by surrogates,, Structural and Multidisciplinary Optimization, 17 (1999), 1. 
[3] 
T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering,, SIAM Journal on Optimization, 10 (2000), 1149. doi: 10.1137/S1052623499354096. 
[4] 
B. Colson, P. Marcotte and G. Savard, Bilevel programming: A survey,, 4OR: A Quarterly Journal of Operations Research, 3 (2005), 87. 
[5] 
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "TrustRegion Methods,'', SIAM, (2000). doi: 10.1137/1.9780898719857. 
[6] 
A. R. Conn and Ph. L. Toint, An algorithm using quadratic interpolation for unconstrained derivative free optimization,, in, (1996), 27. 
[7] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization algorithm in practice,, the American Institute of Aeronautics and Astronautics Conference, (1998). 
[8] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization method via support vector machines,, 1999. Available from: , (). 
[9] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, On the convergence of derivativefree methods for unconstrained optimization,, in, (1997), 83. 
[10] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of interpolation sets in derivative free optimization,, Mathematical Programming, 111 (2008), 141. doi: 10.1007/s1010700600735. 
[11] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of sample sets in derivative free optimization: Polynomial regression and underdetermined interpolation,, IMA Journal of Numerical Analysis, 28 (2008), 721. doi: 10.1093/imanum/drn046. 
[12] 
C. Cox and M. Rubinstein, "Option Markets,'', PrenticeHall, (1985). 
[13] 
N. Cristianini and J. ShaweTaylor, "An Introduction to Support Vector Machines and Other Kernelbased Methods,'', Cambridge University Press, (2000). 
[14] 
J. E. Dennis and V. Torczon, Direct search methods on parallel machines,, SIAM Journal on Optimization, 1 (1991), 448. doi: 10.1137/0801027. 
[15] 
R. A. Fisher, "The Design of Experiments,'', Oliver and Boyd Ltd., (1951). 
[16] 
P. Gilmore and C. T. Kelley, An implicit filtering algorithm for optimization of functions with many local minima,, SIAM Journal on Optimization, 5 (1995), 269. doi: 10.1137/0805015. 
[17] 
B. Karasözen, Survey of trustregion derivative free optimization methods,, Journal of Industrial and Management Optimization, 3 (2007), 321. 
[18] 
T. G. Kolda, R. M. Lewis and V. Torzcon, Optimization by direct search: new perspectives of some classical and modern methods,, SIAM Review, 45 (2003), 385. doi: 10.1137/S003614450242889. 
[19] 
J. A. Nelder and R. Mead, A simplex method for function minimization,, Computer Journal, 7 (1965), 308. 
[20] 
J. Nocedal and S. J. Wright, "Numerical Optimization,'', SpringerVerlag, (1999). doi: 10.1007/b98874. 
[21] 
M. J. D. Powell, Trust region methods that employ quadratic interpolation to the objective function,, Presentation at the 5th SIAM Conference on Optimization, (1996). 
[22] 
M. J. D. Powell, UOBYQA: unconstrained optimization by quadratic approximation,, Mathematical Programming, 92 (2002), 555. doi: 10.1007/s101070100290. 
[23] 
J. A. Tilley, Valuing American options in a path simulation model,, Transactions of the Society of Actuaries, 45 (1993), 83. 
[24] 
V. Torczon, On the convergence of the multidirectional search algorithm,, SIAM Journal on Optimization, 1 (1991), 123. doi: 10.1137/0801010. 
[25] 
D. Winfield, "Function and Functional Optimization by Interpolation in Data Tables,'', PhD thesis, (1969). 
[26] 
D. Winfield, Functional minimization by interpolation in a data table,, Journal of the Institute of Mathematics and its Applications, 12 (1973), 339. doi: 10.1093/imamat/12.3.339. 
show all references
References:
[1] 
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and unconstrained testing environment,, ACM Transactions on Mathematical Software, 21 (1995), 123. doi: 10.1145/200979.201043. 
[2] 
A. J. Booker, J. E. Dennis, P. D. Frank, D. B. Serafini, V. Torczon and M. W. Trosset, A rigorous framework for optimization of expensive functions by surrogates,, Structural and Multidisciplinary Optimization, 17 (1999), 1. 
[3] 
T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering,, SIAM Journal on Optimization, 10 (2000), 1149. doi: 10.1137/S1052623499354096. 
[4] 
B. Colson, P. Marcotte and G. Savard, Bilevel programming: A survey,, 4OR: A Quarterly Journal of Operations Research, 3 (2005), 87. 
[5] 
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "TrustRegion Methods,'', SIAM, (2000). doi: 10.1137/1.9780898719857. 
[6] 
A. R. Conn and Ph. L. Toint, An algorithm using quadratic interpolation for unconstrained derivative free optimization,, in, (1996), 27. 
[7] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization algorithm in practice,, the American Institute of Aeronautics and Astronautics Conference, (1998). 
[8] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization method via support vector machines,, 1999. Available from: , (). 
[9] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, On the convergence of derivativefree methods for unconstrained optimization,, in, (1997), 83. 
[10] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of interpolation sets in derivative free optimization,, Mathematical Programming, 111 (2008), 141. doi: 10.1007/s1010700600735. 
[11] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of sample sets in derivative free optimization: Polynomial regression and underdetermined interpolation,, IMA Journal of Numerical Analysis, 28 (2008), 721. doi: 10.1093/imanum/drn046. 
[12] 
C. Cox and M. Rubinstein, "Option Markets,'', PrenticeHall, (1985). 
[13] 
N. Cristianini and J. ShaweTaylor, "An Introduction to Support Vector Machines and Other Kernelbased Methods,'', Cambridge University Press, (2000). 
[14] 
J. E. Dennis and V. Torczon, Direct search methods on parallel machines,, SIAM Journal on Optimization, 1 (1991), 448. doi: 10.1137/0801027. 
[15] 
R. A. Fisher, "The Design of Experiments,'', Oliver and Boyd Ltd., (1951). 
[16] 
P. Gilmore and C. T. Kelley, An implicit filtering algorithm for optimization of functions with many local minima,, SIAM Journal on Optimization, 5 (1995), 269. doi: 10.1137/0805015. 
[17] 
B. Karasözen, Survey of trustregion derivative free optimization methods,, Journal of Industrial and Management Optimization, 3 (2007), 321. 
[18] 
T. G. Kolda, R. M. Lewis and V. Torzcon, Optimization by direct search: new perspectives of some classical and modern methods,, SIAM Review, 45 (2003), 385. doi: 10.1137/S003614450242889. 
[19] 
J. A. Nelder and R. Mead, A simplex method for function minimization,, Computer Journal, 7 (1965), 308. 
[20] 
J. Nocedal and S. J. Wright, "Numerical Optimization,'', SpringerVerlag, (1999). doi: 10.1007/b98874. 
[21] 
M. J. D. Powell, Trust region methods that employ quadratic interpolation to the objective function,, Presentation at the 5th SIAM Conference on Optimization, (1996). 
[22] 
M. J. D. Powell, UOBYQA: unconstrained optimization by quadratic approximation,, Mathematical Programming, 92 (2002), 555. doi: 10.1007/s101070100290. 
[23] 
J. A. Tilley, Valuing American options in a path simulation model,, Transactions of the Society of Actuaries, 45 (1993), 83. 
[24] 
V. Torczon, On the convergence of the multidirectional search algorithm,, SIAM Journal on Optimization, 1 (1991), 123. doi: 10.1137/0801010. 
[25] 
D. Winfield, "Function and Functional Optimization by Interpolation in Data Tables,'', PhD thesis, (1969). 
[26] 
D. Winfield, Functional minimization by interpolation in a data table,, Journal of the Institute of Mathematics and its Applications, 12 (1973), 339. doi: 10.1093/imamat/12.3.339. 
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