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Applying the pattern search implicit filtering algorithm for solving a noisy problem of parameter identification. (English) Zbl 1446.90147
Summary: Our contribution in this paper is twofold. First, the global convergence analysis of the recently proposed pattern search implicit filtering algorithm (PSIFA), aimed at linearly constrained noisy minimization problems, is revisited to address more general locally Lipschitz objective functions corrupted by noise. Second, PSIFA is applied for solving the damped harmonic oscillator parameter identification problem. This problem can be formulated as a linearly constrained optimization problem, for which the constraints are related to the features of the damping. Such a formulation rests upon a very expensive objective function whose evaluation comprises the numerical solution of an ordinary differential equation (ODE), with intrinsic numerical noise. Computational experimentation encompasses distinct choices for the ODE solvers, and a comparative analysis of the most effective options against the pattern search and the implicit filtering algorithms.
90C30 Nonlinear programming
90C56 Derivative-free methods and methods using generalized derivatives
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
Full Text: DOI
[1] Audet, C.; Dennis, JE Jr, Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim., 17, 1, 188-217 (2006) · Zbl 1112.90078
[2] Audet, C.; Dennis, JE Jr, A progressive barrier for derivative-free nonlinear programming, SIAM J. Optim., 20, 1, 445-472 (2009) · Zbl 1187.90266
[3] Audet, C.; Hare, W., Derivative-Free and Blackbox Optimization. Springer Series in Operations Research and Financial Engineering (2017), Cham: Springer International Publishing, Cham · Zbl 1391.90001
[4] Bertsekas, DP, Nonlinear Programming (1999), Belmont: Athena Scientific, Belmont
[5] Clarke, FH, Optimization and Nonsmooth Analysis (1990), Philadelphia: SIAM, Philadelphia
[6] Conn, AR; Scheinberg, K.; Vicente, LN, Introduction to Derivative-Free Optimization (2009), Philadelphia: SIAM, Philadelphia
[7] Custódio, AL; Dennis, JE Jr; Vicente, LN, Using simplex gradients of nonsmooth functions in direct search methods, IMA J. Numer. Anal., 28, 4, 770-784 (2008) · Zbl 1156.65059
[8] Custódio, AL; Vicente, LN, Using sampling and simplex derivatives in pattern search methods, SIAM J. Optim., 18, 2, 537-555 (2007) · Zbl 1144.65039
[9] Diniz-Ehrhardt, MA; Ferreira, DG; Santos, SA, A pattern search and implicit filtering algorithm for solving linearly constrained minimization problems with noisy objective functions, Optim. Methods Softw., 34, 4, 827-852 (2019) · Zbl 1415.90148
[10] Diniz-Ehrhardt, MA; Martínez, JM; Raydan, M., A derivative-free nonmonotone line-search technique for unconstrained optimization, J. Comput. Appl. Math., 219, 2, 383-397 (2008) · Zbl 1149.65041
[11] Dolan, ED; Moré, JJ, Benchmarking optimization software with performance profiles, Math. Program., 91, 2, 201-213 (2002) · Zbl 1049.90004
[12] Fasano, G.; Liuzzi, G.; Lucidi, S.; Rinaldi, F., A linesearch-based derivative-free approach for nonsmooth constrained optimization, SIAM J. Optim., 24, 3, 959-992 (2014) · Zbl 1302.90207
[13] Finkel, DE; Kelley, CT, Convergence analysis of sampling methods for perturbed Lipschitz functions, Pac. J. Optim., 5, 2, 339-350 (2009)
[14] Gilmore, P.; Kelley, CT, An implicit filtering algorithm for optimization of functions with many local minima, SIAM J. Optim., 5, 2, 269-285 (1995) · Zbl 0828.65064
[15] Gonçalves, D.F.: Derivative-free methods for nonlinear programming: linearly constrained problems with noise objective function. Ph.D. thesis, Institute of Mathematics, University of Campinas, Campinas (SP), Brazil (2017) (in Portughese)
[16] Gratton, S., Royer, C.W., Vicente, L.N., Zhang, Z.: Direct search based on probabilistic feasible descent for bound and linearly constrained problems. preprint 17-10, Department of Mathematics, University of Coimbra (2017) · Zbl 1420.90083
[17] Hock, W., Schittkowski, K.: Test examples for nonlinear programming codes. In: Lecture Notes in Economics and Mathematical Systems, vol. 187. Springer (1981) · Zbl 0452.90038
[18] Kelley, CT, Iterative Methods for Optimization (1999), Philadelphia: SIAM, Philadelphia
[19] Kelley, CT, Implicit Filtering (2011), Philadelphia: SIAM, Philadelphia
[20] Kolda, TG; Lewis, RM; Torczon, V., Optimization by direct search: new perspectives on some classical and modern methods, SIAM Rev., 45, 3, 385-482 (2003) · Zbl 1059.90146
[21] Lewis, RM; Shepherd, A.; Torczon, V., Implementing generating set search methods for linearly constrained minimization, SIAM J. Sci. Comput., 29, 6, 2507-2530 (2007) · Zbl 1166.90368
[22] Lewis, RM; Torczon, V., Pattern search methods for linearly constrained minimization, SIAM J. Optim., 10, 3, 917-941 (2000) · Zbl 1031.90048
[23] Lucidi, S.; Sciandrone, M.; Tseng, P., Objective-derivative-free methods for constrained optimization, Math. Program., 92, 1, 37-59 (2002) · Zbl 1024.90062
[24] Moler, CB, Numerical Computing with MATLAB (2004), Philadelphia: SIAM, Philadelphia · Zbl 1059.68162
[25] Moré, JJ; Wild, SM, Benchmarking derivative-free optimization algorithms, SIAM J. Optim., 20, 1, 172-191 (2009) · Zbl 1187.90319
[26] Rill, G., Road Vehicle Dynamics: Fundamentals and Modeling (2011), Boca Raton: CRC Press, Boca Raton
[27] Shampine, LF; Reichelt, MW, The MATLAB ODE suite, SIAM J. Sci. Comput., 18, 1, 1-22 (1997) · Zbl 0868.65040
[28] Stoneking, DE; Bilbro, GL; Gilmore, PA; Trew, RJ; Kelley, CT, Yield optimization using a gaas process simulator coupled to a physical device model, IEEE Trans. Microw. Theory Tech., 40, 7, 201-213 (1992)
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