A pattern search and implicit filtering algorithm for solving linearly constrained minimization problems with noisy objective functions

Applying the pattern search implicit filtering algorithm for solving a noisy problem of parameter identification

“…We have recently developed a globally convergent derivative-free algorithm that combines pattern search [21,22] and implicit filtering [19] elements. Named PSIFA, that stands for pattern search implicit filtering algorithm, it was created for addressing linearly constrained problems with noisy objective functions [9]. The global convergence analysis of PSIFA was developed under the assumption that the noise decays as the generated sequence approaches optimality.…”

“…The global convergence analysis of PSIFA was developed under the assumption that the noise decays as the generated sequence approaches optimality. In [9] we have also presented numerical experiments in matlab with problems from the literature [17], for which we have added a synthetic noise, fulfilling the assumptions of the convergence analysis. Besides, we have solved problems with controlled degree of degeneracy, with synthetic noise and also with white noise, without satisfying the global convergence assumption.…”

“…In this work, the global convergence results of [9] have been revisited, assuming the objective function to be the sum of a locally Lipschitz continuous term with a low amplitude and high frequency noise. Moreover, to assess the performance of PSIFA for a problem with inherent noise, we have considered a simple parameter identification problem, motivated by a case study of Kelley's book [19], with an enlarged setting.…”

“…In Sect. 2 we provide the main ingredients of the problem and recall the notation from [9]. The algorithm PSIFA is 1 3 Applying the pattern search implicit filtering algorithm… presented in Sect.…”

“…We stress that our approach does not require the iterates to lie on a rational lattice, as in [21,22], neither depends on compact simple bounds for rescaling the problem variables, as assumed in [19]. In [9], specific tools and results have been developed, accompanied by an original theoretical analysis. Nevertheless, as the first term of the objective function was assumed to be smooth, not all the results and proofs will follow straightforwardly upon the local Lipschitz continuity of such a term.…”