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http://hdl.handle.net/10397/93911
Title: | A smoothing direct search method for Monte Carlo-based bound constrained composite nonsmooth optimization | Authors: | Chen, X Kelley, CT Xu, F Zhang, Z |
Issue Date: | 2018 | Source: | SIAM journal on scientific computing, 2018, v. 40, no. 4, p. A2174-A2199 | Abstract: | We propose and analyze a smoothing direct search algorithm for finding a minimizer of a nonsmooth nonconvex function over a box constraint set, where the objective function values cannot be computed directly but are approximated by Monte Carlo simulation. In the algorithm, we adjust the stencil size, the sample size, and the smoothing parameter simultaneously so that the stencil size goes to zero faster than the smoothing parameter and the square root of the sample size goes to infinity faster than the reciprocal of the stencil size. We prove that with probability one any accumulation point of the sequence generated by the algorithm is a Clarke stationary point. We report on numerical results from statistics and financial applications. | Keywords: | Clarke stationarity Direct search algorithm Monte Carlo simulation Nonsmooth optimization Sampling methods Smoothing functions |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on scientific computing | ISSN: | 1064-8275 | EISSN: | 1095-7197 | DOI: | 10.1137/17M1116714 | Rights: | © 2018 Society for Industrial and Applied Mathematics The following publication Chen, X., Kelley, C. T., Xu, F., & Zhang, Z. (2018). A smoothing direct search method for Monte Carlo-based bound constrained composite nonsmooth optimization. SIAM Journal on Scientific Computing, 40(4), A2174-A2199 is available at https://doi.org/10.1137/17M1116714 |
Appears in Collections: | Journal/Magazine Article |
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