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

被引：5
作者：
迟晓妮 [1 ]
韦洪锦 [2 ]
万仲平 [3 ]
朱志斌 [4 ]
机构：
[1] School of Mathematics and Computing Science, Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology
[2] School of Mathematics and Computing Science, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology
[3] School of Mathematics and Statistics, Wuhan University
[4] School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic
来源：
Acta Mathematica Scientia(English Series) | 2017年 / 37卷 / 05期
关键词：
D O I：
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中图分类号：
O221 [规划论（数学规划）];
学科分类号：
摘要：
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.
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页码：1262 / 1280
页数：19
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