| 二次半定规划的原始对偶预估校正内点算法 |
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| 引用本文： | 黄静静,商朋见,王爱文.二次半定规划的原始对偶预估校正内点算法[J].北方交通大学学报,2011(3):136-141. |
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| 作者姓名： | 黄静静 商朋见 王爱文 |
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| 作者单位： | [1]北京交通大学理学院,北京100044 [2]北京信息科技大学理学院,北京100192 |
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| 基金项目： | 国家自然科学基金资助项目（60772036,61071142）; 教育部博士点基金项目资助（20070004002）; 北京市教委面上项目资助（201110772019）; 北京信息科技大学校科研基金资助项目 |
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| 摘 要： | 将半定规划（Semidefinite Programming,SDP）的内点算法推广到二次半定规划（QuadraticSemidefinite Programming,QSDP）,重点讨论了AHO搜索方向的产生方法.首先利用Wolfe对偶理论推导得到了求解二次半定规划的非线性方程组,利用牛顿法求解该方程组,得到了求解QSDP的内点算法的AHO搜索方向,证明了该搜索方向的存在唯一性,最后给出了求解二次半定规划的预估校正内点算法的具体步骤,并对基于不同搜索方向的内点算法进行了数值实验,结果表明基于NT方向的内点算法最为稳健.
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| 关 键 词： | 半定规划 二次半定规划 内点算法 搜索方向 牛顿法 |
Primal-dual predictor-corrector interior point algorithm for quadratic semidefinite programming |
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| HUANG Jingjing,SHANG Pengjian,WANG Aiwen.Primal-dual predictor-corrector interior point algorithm for quadratic semidefinite programming[J].Journal of Northern Jiaotong University,2011(3):136-141. |
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| Authors: | HUANG Jingjing SHANG Pengjian WANG Aiwen |
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| Institution: | 1.School of Science,Beijing Jiaotong University,Beijing 100044,China;2.School of Science,Beijing Information and Science Technology University,Beijing 100192,China) |
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| Abstract: | This paper extends the interior point algorithm for solving Semidefinite Programming（SDP） to Quadratic Semidefinite Programming（QSDP） and especially discusses the generation of AHO search direction.Firstly,we derive the nonlinear equations for solving QSDP using Wolfe＇s dual theorem.The AHO search direction is got by applying Newton＇s method to the equations.Then we prove the existence and uniqueness of the search direction,and give the detaied steps of predictor-corrector interior-point algorithm.At last,this paper provides a numerical comparison of the algoritms using three different search directions and suggests the algorithm using NT direction is the most robust. |
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| Keywords: | semidefinite programming quadratic semidefinite programming interior point algorithm search direction Newton＇s method |
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