张思颖.凸二次规划SDP松弛解的存在性证明[J].重庆工商大学学报(自然科学版),2020,37(3):66-69
ZHANG Si-ying.The Existence Proof of the Solution of SDP Relaxation for Convex Quadratic Program[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2020,37(3):66-69
凸二次规划SDP松弛解的存在性证明
The Existence Proof of the Solution of SDP Relaxation for Convex Quadratic Program
  
DOI:
中文关键词:  二次规划  强对偶定理  Gershgorin圆盘定理
英文关键词:quadratic program  strong duality theorem  Gershgorin circle theorem
基金项目:
作者单位
张思颖 重庆师范大学 数学科学学院重庆 401331 
摘要点击次数: 28
全文下载次数: 18
中文摘要:
      针对利用CVX软件求解半定规划问题的有效性依赖于该半定规划问题的原始-对偶性,提出利用半定规划问题的强对偶定理和Gershgorin圆盘定理证明在箱子约束及单位球形约束下的凸二次规划问题的半定规划松弛模型解的存在性。该证明方法为嵌入了SeDuMi和SDPT3这两种内点算法的CVX软件提供了有效求解半定规划松弛模型的理论依据;一旦利用该方法证明了半定规划问题解的存在,必然可利用CVX软件有效求解。
英文摘要:
      Because the problem of quadratic program has received extensive attention and research in the field of continuous and combinatorial optimization since the semi definite planning (SDP) relaxation method was proposed, because the effectiveness of the solution of SDP by using CVX software relies on the primal SDP and dual SDP, this paper proposes to use the strong duality theorem and Gershgorin circle theorem to prove the existence of the solution of SDP relaxation model of convex quadratic program under the condition of box constraints and unit spherical constraints. The new proof method of the existence of the solution of the SDP lays the theoretical foundation of the effectiveness for solving the SDP relaxation model by the CVX software with the two kinds of interior point algorithms of SeDuMi and SDPT3. Once this method is used to prove the existence of the solution of SDP, it is necessary to use CVX software to receive effective solution.
查看全文  查看/发表评论  下载PDF阅读器
关闭
重庆工商大学学报自然科学版 版权所有
地址:中国 重庆市 南岸区学府大道19号,重庆工商大学学报编辑部 邮编:400067
电话:023-62769495 传真:
您是第1872958位访客
关注微信二维码