A subgradient method based on gradient sampling for solving convex optimization problems

Yaohua Hu, Chee-Khian Sim, Xiaoqi Yang

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Abstract

Based on the gradient sampling technique, we present a subgradient algorithm to solve the nondifferentiable convex optimization problem with an extended real-valued objective function. A feature of our algorithm is the approximation of subgradient at a point via random sampling of (relative) gradients at nearby points, and then taking convex combinations of these (relative) gradients. We prove that our algorithm converges to an optimal solution with probability 1. Numerical results demonstrate that our algorithm performs favourably compared with existing subgradient algorithms on applications considered.
Original languageEnglish
Pages (from-to)1559-1584
Number of pages26
JournalNumerical Functional Analysis and Optimization
Volume36
Issue number12
Early online date9 Dec 2015
DOIs
Publication statusPublished - 31 Dec 2015

Keywords

  • Gradient sampling technique
  • Subgradient method
  • Projection
  • Convex optimization

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