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October  2016, 12(4): 1349-1366. doi: 10.3934/jimo.2016.12.1349

A subgradient-based convex approximations method for DC programming and its applications

 1 School of Sciences, Dalian Ocean University, Dalian 116023, China 2 School of Mathematical Sciences, Dalian University of Technology, Dalian 116023

Received  September 2014 Revised  May 2015 Published  January 2016

We consider an optimization problem that minimizes a function of the form $f=f_0+f_1-f_2$ with the constraint $g-h\leq 0$, where $f_0$ is continuous differentiable, $f_1,f_2$ are convex and $g,h$ are lower semicontinuous convex. We propose to solve the problem by an inexact subgradient-based convex approximations method. Under mild assumptions, we show that the method is guaranteed to converge to a stationary point. Finally, some preliminary numerical results are given.
Citation: Jian Gu, Xiantao Xiao, Liwei Zhang. A subgradient-based convex approximations method for DC programming and its applications. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1349-1366. doi: 10.3934/jimo.2016.12.1349
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