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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.
MSC:
90C30 Nonlinear programming
90C56 Derivative-free methods and methods using generalized derivatives
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
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