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Alvaro Maggiar (alvaro.maggiaru.northwestern.edu) Abstract: In this paper we consider the optimization of a functional $F$ defined as the co nvolution of a function $f$ with a Gaussian kernel. We propose this type of objective function for the optimization of the output of complex computational simulations, which often present some form of deterministic noise and need to be smoothed for the results to be meaningful. We introduce a derivativefree algorithm that computes trial points from the minimization of a regression model of the noisy function $f$ over a trust region. The regression model is constructed from function values at sample points that are chosen randomly around iterates and trial points of the algorithm. The weights given to the individual sample points in the regression problem are obtained according to an adaptive multiple importance sampling strategy. This has two advantages. First, it makes it possible to reuse all noisy function values collected over the course of the optimization. Second, the resulting regression model converges to the secondorder Taylor approximation of the convolution functional $F$. We prove that, with probability one, each limit point of the iterates is a stationary point of $F$. Computational experiments on a set of benchmark problems with noisy functions compare the proposed algorithm with the deterministic derivativefree trustregion method the proposed method is based on. It is demonstrated that the proposed algorithm performs similarly efficiently in the early stages of the optimization and is able to overcome convergence problems of the original method, which might get trapped in spurious local minima induced by the noise. Keywords: Category 1: Nonlinear Optimization Citation: Technical Report IEMS Department Northwestern University Download: [PDF] Entry Submitted: 07/20/2015 Modify/Update this entry  
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