SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

doi:10.1016/S0252-9602(17)30072-3

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1262-1280.doi: 10.1016/S0252-9602(17)30072-3

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SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

Xiaoni CHI¹, Hongjin WEI², Zhongping WAN³, Zhibin ZHU⁴

1. School of Mathematics and Computing Science, Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin 541004, China;
2. School of Mathematics and Computing Science, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin 541004, China;
3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
4. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China

Received:2016-05-10 Revised:2016-12-16 Online:2017-10-25 Published:2017-10-25
Contact: Xiaoni CHI,E-mail:chixiaoni@126.com E-mail:chixiaoni@126.com
Supported by:
This research was supported by the National Natural Science Foundation of China (11401126, 71471140 and 11361018), Guangxi Natural Science Foundation (2016GXNSFBA380102 and 2014GXNSFFA118001), Guangxi Key Laboratory of Cryptography and Information Security (GCIS201618), and Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ15112 and YQ16112), China.

Abstract

Abstract:

In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming (CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone (SOC), we reformulate the CCP problem as the second-order cone problem (SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.

Key words: circular cone programming, second-order cone programming, nonmonotone line search, smoothing Newton method, local quadratic convergence

Xiaoni CHI, Hongjin WEI, Zhongping WAN, Zhibin ZHU. SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH[J].Acta mathematica scientia,Series B, 2017, 37(5): 1262-1280.

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SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

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