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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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show all references

References:
[1]

Math. Program., 87 (2000), 401-426. doi: 10.1007/s101070050003.  Google Scholar

[2]

European J. Oper. Res., 183 (2007), 1067-1085. doi: 10.1016/j.ejor.2005.07.028.  Google Scholar

[3]

Ann. Oper. Res., 133 (2005), 23-46. doi: 10.1007/s10479-004-5022-1.  Google Scholar

[4]

Math. Program., 87 (2000), 131-152.  Google Scholar

[5]

{Springer, New York}, 2000. doi: 10.1007/978-1-4612-1394-9.  Google Scholar

[6]

Nonliner Anal., 75 (2012), 3672-3681. doi: 10.1016/j.na.2012.01.023.  Google Scholar

[7]

PhD thesis, Stanford University, 2002. Google Scholar

[8]

PhD thesis, National University of Singapore, 2010. Google Scholar

[9]

SIAM J. Optim., 19 (2008), 503-523. doi: 10.1137/070679041.  Google Scholar

[10]

Oper. Res., 59 (2011), 617-630. doi: 10.1287/opre.1100.0910.  Google Scholar

[11]

J. Optim. Theory Appl., 103 (1999), 1-43. doi: 10.1023/A:1021765131316.  Google Scholar

[12]

IEEE Signal Process Mag., 27 (2010), 20-34. doi: 10.1109/MSP.2010.936019.  Google Scholar

[13]

SIAM J. Optim., 18 (2007), 1-28. doi: 10.1137/050642691.  Google Scholar

[14]

Springer, Berlin, 2006.  Google Scholar

[15]

SIAM J. Optim., 17 (2006), 969-996. doi: 10.1137/050622328.  Google Scholar

[16]

SIAM Rev., 52 (2010), 471-501. doi: 10.1137/070697835.  Google Scholar

[17]

Springer, New York, 1998. doi: 10.1007/978-3-642-02431-3.  Google Scholar

[18]

Springer, Berlin, 2007. doi: 10.1007/978-3-540-71333-3.  Google Scholar

[19]

J. Optim. Theory Appl., 59 (2014), 181-199. doi: 10.1007/s10957-013-0513-3.  Google Scholar

[20]

SIAM, Philadelphia, 2009. doi: 10.1137/1.9780898718751.  Google Scholar

[21]

IEEE Trans. Signal Process., 54 (2006), 2239-2251. doi: 10.1109/TSP.2006.872578.  Google Scholar

[22]

J. Optim. Theory Appl., 147 (2010), 263-277. doi: 10.1007/s10957-010-9721-2.  Google Scholar

[23]

J. Ind. Manag. Optim., 8 (2012), 733-747. doi: 10.3934/jimo.2012.8.733.  Google Scholar

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