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A derivative-free trust-region algorithm for unconstrained optimization with controlled error
1. | Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501,, Japan |
2. | Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501 |
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), 123-160.
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), 1-13. |
[3] |
T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering, SIAM Journal on Optimization, 10 (2000), 1149-1162.
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), 87-107. |
[5] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods,'' SIAM, Philadelphia, 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 "Nonlinear Optimization and Applications,'' Plenum Publishing, (1996), 27-47. |
[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, St Louis, 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 derivative-free methods for unconstrained optimization, in "Approximation Theory and Optimization,'' Cambridge University Press, (1997), 83-108. |
[10] |
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of interpolation sets in derivative free optimization, Mathematical Programming, 111 (2008), 141-172.
doi: 10.1007/s10107-006-0073-5. |
[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), 721-748.
doi: 10.1093/imanum/drn046. |
[12] |
C. Cox and M. Rubinstein, "Option Markets,'' Prentice-Hall, 1985. |
[13] |
N. Cristianini and J. Shawe-Taylor, "An Introduction to Support Vector Machines and Other Kernel-based Methods,'' Cambridge University Press, Cambridge, UK, 2000. |
[14] |
J. E. Dennis and V. Torczon, Direct search methods on parallel machines, SIAM Journal on Optimization, 1 (1991), 448-474.
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), 269-285.
doi: 10.1137/0805015. |
[17] |
B. Karasözen, Survey of trust-region derivative free optimization methods, Journal of Industrial and Management Optimization, 3 (2007), 321-334. |
[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), 385-482.
doi: 10.1137/S003614450242889. |
[19] |
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308-313. |
[20] |
J. Nocedal and S. J. Wright, "Numerical Optimization,'' Springer-Verlag, New York, 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), 555-582.
doi: 10.1007/s101070100290. |
[23] |
J. A. Tilley, Valuing American options in a path simulation model, Transactions of the Society of Actuaries, 45 (1993), 83-104. |
[24] |
V. Torczon, On the convergence of the multidirectional search algorithm, SIAM Journal on Optimization, 1 (1991), 123-145.
doi: 10.1137/0801010. |
[25] |
D. Winfield, "Function and Functional Optimization by Interpolation in Data Tables,'' PhD thesis, Harvard University in Cambridge, 1969. |
[26] |
D. Winfield, Functional minimization by interpolation in a data table, Journal of the Institute of Mathematics and its Applications, 12 (1973), 339-347.
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), 123-160.
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), 1-13. |
[3] |
T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering, SIAM Journal on Optimization, 10 (2000), 1149-1162.
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), 87-107. |
[5] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods,'' SIAM, Philadelphia, 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 "Nonlinear Optimization and Applications,'' Plenum Publishing, (1996), 27-47. |
[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, St Louis, 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 derivative-free methods for unconstrained optimization, in "Approximation Theory and Optimization,'' Cambridge University Press, (1997), 83-108. |
[10] |
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of interpolation sets in derivative free optimization, Mathematical Programming, 111 (2008), 141-172.
doi: 10.1007/s10107-006-0073-5. |
[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), 721-748.
doi: 10.1093/imanum/drn046. |
[12] |
C. Cox and M. Rubinstein, "Option Markets,'' Prentice-Hall, 1985. |
[13] |
N. Cristianini and J. Shawe-Taylor, "An Introduction to Support Vector Machines and Other Kernel-based Methods,'' Cambridge University Press, Cambridge, UK, 2000. |
[14] |
J. E. Dennis and V. Torczon, Direct search methods on parallel machines, SIAM Journal on Optimization, 1 (1991), 448-474.
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), 269-285.
doi: 10.1137/0805015. |
[17] |
B. Karasözen, Survey of trust-region derivative free optimization methods, Journal of Industrial and Management Optimization, 3 (2007), 321-334. |
[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), 385-482.
doi: 10.1137/S003614450242889. |
[19] |
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308-313. |
[20] |
J. Nocedal and S. J. Wright, "Numerical Optimization,'' Springer-Verlag, New York, 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), 555-582.
doi: 10.1007/s101070100290. |
[23] |
J. A. Tilley, Valuing American options in a path simulation model, Transactions of the Society of Actuaries, 45 (1993), 83-104. |
[24] |
V. Torczon, On the convergence of the multidirectional search algorithm, SIAM Journal on Optimization, 1 (1991), 123-145.
doi: 10.1137/0801010. |
[25] |
D. Winfield, "Function and Functional Optimization by Interpolation in Data Tables,'' PhD thesis, Harvard University in Cambridge, 1969. |
[26] |
D. Winfield, Functional minimization by interpolation in a data table, Journal of the Institute of Mathematics and its Applications, 12 (1973), 339-347.
doi: 10.1093/imamat/12.3.339. |
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