解非线性半定规划的一种回溯线搜索型算法  

A Backtracking Line Search Method for Nonlinear Semidefinite Programming

作　　者：李丹丹 王松华 李远飞 LI Dandan;WANG Songhua;LI Yuanfei(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;School of Mathematics and Statistics,Baise University,Baise Guangxi 533000,China)

机构地区：[1]广州华商学院应用数学系,广州511300 [2]百色学院数学与统计学院,广西百色533000

出　　处：《西南师范大学学报（自然科学版）》2022年第3期61-71,共11页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：广西自然科学基金项目(2020GXNSFAA159069);广东省普通高校创新团队项目(2020WCXTD008);广州华商学院校内项目(2021HSDS32)。

摘　　要：为避免罚函数和滤子的缺点,提高带有等式约束和半负定矩阵约束的非线性半定规划求解效率,本文通过二次半定子问题构建搜索方向,结合回溯线搜索技术和非单调充分下降性条件,提出了一种新的无罚函数无滤子的线搜索型序列半定规划算法.在合理的假设条件下,证明了新算法的适定性以及全局收敛性,最后通过初步的数值试验验证了新算法的有效性.In order to avoid the fault of penalty function and filter and improve the efficiency of solving nonlinear semidefinite programming with equality constraints and matrix inequality constraints,by computing a search direction by quadratic semidefinite subproblem and adopting backtracking line search technique and nonmonotonically sufficient descent trait,a sequential semidefinite programming algorithm without penalty function and filter on the line search method has been put forward.Under some reasonable assumptions,the proposed algorithm is well defined and globally convergent.Finally,the preliminary numerical results show that it is highly efficient.

关 键 词：序列半定规划 回溯线搜索 非单调 全局收敛性 

分 类 号：O221[理学—运筹学与控制论]