A smoothing direct search method for Monte Carlo-based bound constrained composite nonsmooth optimization

Xiaojun Chen, C. T. Kelley, Fengmin Xu, Zaikun Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)A2174-A2199
JournalSIAM Journal on Scientific Computing
Issue number4
Publication statusPublished - 1 Jan 2018


  • Clarke stationarity
  • Direct search algorithm
  • Monte Carlo simulation
  • Nonsmooth optimization
  • Sampling methods
  • Smoothing functions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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