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

作     者：迟晓妮 韦洪锦 万仲平 朱志斌 

作者机构：School of Mathematics and Computing ScienceGuangxi Key Laboratory of Cryptography and Information SecurityGuilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computing ScienceGuangxi Key Laboratory of Automatic Detecting Technology and InstrumentsGuilin University of Electronic TechnologyGuilin 541004China School of Mathematics and StatisticsWuhan UniversityWuhan 430072China School of Mathematics and Computing ScienceGuangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilin 541004China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2017年第37卷第5期

页      面：1262-1280页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：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) Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112) China 

主　　题：circular cone programming second-order cone programming nonmonotone line search smoothing Newton method local quadratic convergence 

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.