非线性半定规划的一个线搜索精确罚方法
A Line Search Exact Penalty Method for Nonlinear Semidefinite Programming
DOI: 10.12677/AAM.2019.84071, PDF,    国家自然科学基金支持
作者: 吴加其, 黎健玲：广西大学数学与信息科学学院，广西 南宁
关键词: 非线性半定规划；线搜索；罚函数；全局收敛性；Nonlinear Semidefinite Programming； Line Search； Penalty Function； Global Convergence
摘要: 本文提出了一个求解非线性半定规划的线搜索精确罚函数方法。在每次迭代中通过求解一个二次半定规划产生搜索方向，某个精确罚函数作为效益函数用于线搜索确定步长。且借助信赖域子问题的最优解更新罚参数。在较温和的条件下本文证明了算法具有全局收敛性。
Abstract: This paper presents a line search exact penalty method for nonlinear semidefinite programming. At each iteration, the search direction is determined by solving a quadratic semidefinite programming subproblem. Certain exact penalty function is used as merit function for line search and a step size is obtained. The penalty parameter is updated by the optimal solution of the trust region subproblem. Under some appropriate conditions, the global convergence of the proposed algorithm is proved.
文章引用：吴加其, 黎健玲. 非线性半定规划的一个线搜索精确罚方法[J]. 应用数学进展, 2019, 8(4): 638-649. https://doi.org/10.12677/AAM.2019.84071

参考文献

[1] Ben-Tal, A., Jarre, F., Kocvara, M., Nemirovski, A. and Zowe, J. (2000) Optimal Design of Trusses under a Nonconvex Global Buckling Constraint. Optimization and Engineering, 1, 189-213. [Google Scholar] [CrossRef] 
[2] Fares, B., Noll, D. and Apkarian, P. (2002) Robust Control via Sequential Semidefinite Programming. SIAM Journal on Control and Optimization, 40, 1791-1820. [Google Scholar] [CrossRef] 
[3] Kocvara, M. and Stingl, M. (2004) Solving Nonconvex SDP Problems of Structural Optimization with Stability Control. Optimization Methods and Software, 19, 595-609. [Google Scholar] [CrossRef] 
[4] Correa, R. and Ramirez, H.C. (2004) A Global Algorithm for Nonlinear Semidefinite Programming. SIAM Journal on Optimization, 15, 303-318. [Google Scholar] [CrossRef] 
[5] Zhao, Q. and Chen, Z.W. (2018) An SQP-Type Method with Superlinear Convergence for Nonlinear Semidefinite Programming. Asia-Pacific Journal of Operational Research, 35, Article ID: 1850009. [Google Scholar] [CrossRef] 
[6] Li, J.L., Yang, Z.P. and Jian, J.B. (2017) A Globally Conver-gent QP-Free Algorithm for Nonlinear Semidefinite Programming. Journal of Inequalities and Application.
[7] 张辉. 非线性半定规划的两个SSDP算法[D]: [硕士学位论文]. 南宁: 广西大学, 2018.
[8] Byrd, R.H., Lopez-Calva, G. and Nocedal, J. (2009) A Line Search Exact Penalty Method Using Steering Rules. Mathematical Programming, 133, 1-35.
[9] Byrd, R.H., Nocedal, J. and Waltz, R.A. (2008) Steering Exact Penalty Methods for Nonlinear Programming. Optimization Methods and Software, 23, 197-213. [Google Scholar] [CrossRef] 
[10] Leibfritz, F. (2004) COMPlib-Constrained Matrix-Optimization Problem Library. Technical Report.
[11] Gomez, W. and Ramirez, H. (2010) A Filter Algorithm for Nonlinear Semidefinite Programming. Computational and Applied Mathematics, 29, 297-328.
[12] Zhao, Q. and Chen, Z.W. (2016) On the Superlinear Local Convergence of a Penalty-Free Method for Nonlinear Semidefinite Programming. Journal of Computational and Applied Mathematics, 308, 1-19. [Google Scholar] [CrossRef] 

为你推荐