Kvasov: Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems

Kvasov, Dmitri E.:
Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 857-871, (English)
pdf (1.44 MB), djvu (232 Kb). | MR 2455349 | Zbl 1190.65097

Sunto

This paper briefly describes some results of the author's PhD thesis, which has been specially mentioned by the Italian INdAM-SIMAI Committee for the Competition "The Best PhD Thesis in Applied Mathematics defended in 2004-2006". In this work, a global optimization problem is considered where the objective function is a multidimensional black-box function satisfying the Lipschitz condition over a hyperinterval and hard to evaluate. Such functions are frequently encountered in practice that explains a great interest of researchers to the stated problem. A new diagonal scheme which is aimed for developing fast global optimization algorithms is presented, and several such algorithms are introduced and examined. Theoretical and experimental studies performed confirm the benefit of the new approach over traditionally used diagonal global optimization methods.

Referenze Bibliografiche

[1] D. P. BERTSEKAS, Nonlinear Programming, Athena Scientific, Belmont, Massachusetts (1999). | MR 3587371

[2] G. DI PILLO - F. GIANNESSI (Eds.), Nonlinear Optimization and Applications, Plenum Press, New York (1996).

[3] L. C. W. DIXON - G. P. SZEGÖ (Eds.), Towards Global Optimization (Volumes 1 and 2), North-Holland, Amsterdam (1975, 1978). | MR 522648

[4] C. A. FLOUDAS - P. M. PARDALOS (Eds.), Encyclopedia of Optimization (6 Volumes), Kluwer Academic Publishers (2001). | fulltext (doi) | MR 1865755

[5] C. A. FLOUDAS - P. M. PARDALOS - C. ADJIMAN - W. ESPOSITO - Z. GÜMÜS - S. HARDING - J. KLEPEIS - C. MEYER - C. SCHWEIGER, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers (Dordrecht, 1999). | fulltext (doi) | MR 1718483

[6] J. M. GABLONSKY - C. T. KELLEY, A locally-biased form of the DIRECT algorithm, J. Global Optim., 21, 1 (2001), 27-37. | fulltext (doi) | MR 1856800 | Zbl 1039.90049

[7] M. GAVIANO - D. E. KVASOV - D. LERA - YA. D. SERGEYEV, Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization, ACM Trans. Math. Software, 29, 4 (2003), 469-480. | fulltext (doi) | MR 2077342 | Zbl 1068.90600

[8] R. HORST - P. M. PARDALOS (Eds.), Handbook of Global Optimization, Kluwer Academic Publishers, 1 (Dordrecht, 1995). | fulltext (doi) | MR 1377081 | Zbl 0805.00009

[9] R. HORST - H. TUY, Global Optimization - Deterministic Approaches, Springer-Verlag (Berlin, 1996). | fulltext (doi) | MR 1102239 | Zbl 0867.90105

[10] D. R. JONES - C. D. PERTTUNEN - B. E. STUCKMAN, Lipschitzian optimization without the Lipschitz constant, J. Optim. Theory Appl., 79, 1 (1993), 157-181. | fulltext (doi) | MR 1246501 | Zbl 0796.49032

[11] D. E. KVASOV, Algoritmi diagonali di ottimizzazione globale Lipschitziana basati su un'efficiente strategia di partizione, Bollettino U.M.I., 10-A (Serie VIII), 2 (2007), 255-258. In Italian. | fulltext bdim | fulltext EuDML

[12] D. E. KVASOV, Multidimensional Lipschitz global optimization based on efficient diagonal partitions, 4OR - Quart. J. Oper. Res. (2008). To appear. | Zbl 1179.90263

[13] D. E. KVASOV - D. MENNITI - A. PINNARELLI - YA. D. SERGEYEV - N. SORRENTINO, Tuning fuzzy power-system stabilizers in multi-machine systems by global optimization algorithms based on efficient domain partitions, Electr. Power Syst. Res., 78, 7 (2008), 1217-1229.

[14] D. E. KVASOV - C. PIZZUTI - YA. D. SERGEYEV, Local tuning and partition strategies for diagonal GO methods, Numer. Math., 94, 1 (2003), 93-106. | fulltext (doi) | MR 1971214 | Zbl 1056.65059

[15] D. E. KVASOV - YA. D. SERGEYEV, Multidimensional global optimization algorithm based on adaptive diagonal curves, Comput. Math. Math. Phys., 43, 1 (2003) 40-56. | MR 1968767

[16] A. MOLINARO - C. PIZZUTI - YA. D. SERGEYEV, Acceleration tools for diagonal information global optimization algorithms, Comput. Optim. Appl., 18, 1 (2001), 5- 26. | fulltext (doi) | MR 1821077 | Zbl 0963.90060

[17] J. NOCEDAL - S. J. WRIGHT, Numerical Optimization, Springer-Verlag (Dordrecht, 1999). | fulltext (doi) | MR 1713114

[18] P. M. PARDALOS - H. E. ROMEIJN (Eds.), Handbook of Global Optimization, Kluwer Academic Publishers, 2 (Dordrecht, 2002). | fulltext (doi) | MR 1919528

[19] J. D. PINTÉR, Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications), Kluwer Academic Publishers (Dordrecht, 1996). | fulltext (doi) | MR 1374104

[20] J. D. PINTÉR, Global Optimization: Scientific and Engineering Case Studies, Nonconvex Optimization and Its Applications, 85 (Springer-Verlag, Berlin, 2006). | fulltext (doi) | MR 2265360

[21] R. T. ROCKAFELLAR, Convex analysis, Princeton University Press (Princeton, NJ, USA, 1970). | MR 274683 | Zbl 0193.18401

[22] K. SCHITTKOWSKI, More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, 282 (Springer-Verlag, Berlin, 1987). | fulltext (doi) | MR 1117683 | Zbl 0658.90060

[23] YA. D. SERGEYEV, An information global optimization algorithm with local tuning, SIAM J. Optim., 5, 4 (1995), 858-870. | fulltext (doi) | MR 1358808 | Zbl 0847.90128

[24] YA. D. SERGEYEV, A one-dimensional deterministic global minimization algorithm, Comput. Math. Math. Phys., 35, 5 (1995), 705-717. | MR 1337015

[25] YA. D. SERGEYEV, On convergence of ``Divide the Best'' global optimization algorithms, Optimization, 44, 3 (1998), 303-325. | fulltext (doi) | MR 1775619 | Zbl 0986.90058

[26] YA. D. SERGEYEV, An efficient strategy for adaptive partition of N-dimensional intervals in the framework of diagonal algorithms, J. Optim. Theory Appl., 107, 1 (2000), 145-168. | fulltext (doi) | MR 1800933 | Zbl 0969.90068

[27] YA. D. SERGEYEV, Efficient partition of N-dimensional intervals in the framework of one-point-based algorithms, J. Optim. Theory Appl., 124, 2 (2005), 503-510. | fulltext (doi) | MR 2130082 | Zbl 1066.90094

[28] YA. D. SERGEYEV - V. A. GRISHAGIN, Parallel asynchronous global search and the nested optimization scheme, J. Comput. Anal. Appl., 3, 2 (2001), 123-145. | fulltext (doi) | MR 1825071 | Zbl 1033.90093

[29] YA. D. SERGEYEV - D. E. KVASOV, Adaptive diagonal curves and their implementation, The Bulletin of Nizhni Novgorod ``Lobachevsky'' University: Mathematical modelling and optimal control, 2, 24 (2001), 300-317. In Russian.

[30] YA. D. SERGEYEV - D. E. KVASOV, Global search based on efficient diagonal partitions and a set of Lipschitz constants, SIAM J. Optim., 16, 3 (2006), 910-937. | fulltext (doi) | MR 2197562 | Zbl 1097.65068

[31] YA. D. SERGEYEV - D. E. KVASOV, Diagonal Global Optimization Methods, Fiz. Mat. Lit. (Moscow, 2008). In Russian. | fulltext (doi) | MR 3585540 | Zbl 1282.90138

[32] R. G. STRONGIN, Numerical Methods in Multiextremal Problems (Information-Statistical Algorithms), Nauka (Moscow, 1978). In Russian. | MR 509033

[33] R. G. STRONGIN - YA. D. SERGEYEV, Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms, Kluwer Academic Publishers (Dordrecht, 2000). | fulltext (doi) | MR 1797058 | Zbl 0987.90068

[34] A. A. ZHIGLJAVSKY - A. ZILINSKAS, Stochastic Global Optimization, Optimization and Its Applications, 9 (Springer, New York, 2008). | MR 2361744 | Zbl 1136.90003

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche