基于梯度投影的广义滤子填充函数方法
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摘要
本文研究了约束非凸全局优化问题.利用滤子技术和填充函数的架构,提出了一个基于梯度投影的广义滤子填充函数算法,获得了较好的理论性质和数值效果.文章修改了填充函数的定义以及滤子技术的适用范围,推广了局部优化技术,使之成为约束全局问题的有效求解方法之一.
In this paper, non-convex global optimization problems with constraints are studied. By using the structures of filter and filled function, a generalized filter filled function algorithm based on gradient projection is presented and the theoretical properties and numerical results are obtained. The algorithm modifies the definition of the filled function and the application scope of the filter technique, which extends the local optimization technique and makes it one of effective methods to solve the global optimization problems with constraints.
In this paper, non-convex global optimization problems with constraints are studied. By using the structures of filter and filled function, a generalized filter filled function algorithm based on gradient projection is presented and the theoretical properties and numerical results are obtained. The algorithm modifies the definition of the filled function and the application scope of the filter technique, which extends the local optimization technique and makes it one of effective methods to solve the global optimization problems with constraints.
引文
[1] Ge R P. A filled function method for finding a global minimizer of a function of several variables[J]. Math. Prog., 1990, 46(1):191–204.
[2] Zhang L S, Ng C K, Li D, Tian W W. A new filled function method for global optimization[J]. J.Glob. Optim., 2004, 28(1):17–43.
[3] Yang Y J, Shang Y L. A new filled function method for unconstrained global optimization[J]. Appl.Math. Comput., 2005, 173(1):501–512.
[4] Liang Y M, Zhang L S, Li M M, Han B S. A filled function method for global optimization[J]. J.Comput. Appl. Math., 2006, 205(1):16–31.
[5] Wang W, Zhang X S, Li M. A filled function method dominated by filter for nonlinearly global optimization[J]. J. Appl. Math., 2015, 8(3):8–18.
[6] Wu C Z, Kok L T, Volker R. A filled function method for optimal discrete-valued control problems[J]. Glob. Optim., 2009, 44(2):213–225.
[7] Fletcher R, Leyffer S. Nonlinear programming without a penalty function[J]. Math. Prog., 2002,91(2):239–269.
[8] Fletcher R, Leyffer S, Toint P L. On the global convergence of a filter-SQP algorithm[J]. Siam J.Optim., 2006, 13(1):44–59.
[9] Michael U, Stefan U, Luis N V. A globally convergent primal-dual interior-point filter method for nonlinear programming[J]. Math. Prog., 2004, 100(2):379–410.
[10] Andreas W, Lorenz T B. Line search filter methods for nonlinea programming:local convergence[J].SIAM J. Optim., 2005, 16(2):1–31.
[11]胡铨,王薇.求解带箱式约束全局优化问题的滤子填充函数方法[J].运筹学学报, 2016, 03:57–67.
[12] Rosen J B. The gradient projection method for nonlinear programming, Part I. linear constraints[J]. SIAM, 1960, 8(1):181–217.
[13] Zhang X S. On the convergence of Rosen’s gradient projection method:three-dimension case[J].Acta Math. Appl. Sin., Engl. Ser., 1987, 3(3):280–288.
[14] Du D. Remarks on the convergence of Rosen’s gradient projection method[J]. Acta Math. Appl.Sin., Engl. Ser., 1987, 3(3):270–279.
[15] Wang W, Hua S L, Tang J J. A generalized gradient projection filter algorithm for inequality constrained optimization[J]. J. Appl. Math., 2013, 2013(2):4819–4828.
[16] Gao J, Wang W. A generalized gradient projection filter method for arbitrary initial point[J]. Oper.Res. Trans., 2013, 17(2):124–130.
[2] Zhang L S, Ng C K, Li D, Tian W W. A new filled function method for global optimization[J]. J.Glob. Optim., 2004, 28(1):17–43.
[3] Yang Y J, Shang Y L. A new filled function method for unconstrained global optimization[J]. Appl.Math. Comput., 2005, 173(1):501–512.
[4] Liang Y M, Zhang L S, Li M M, Han B S. A filled function method for global optimization[J]. J.Comput. Appl. Math., 2006, 205(1):16–31.
[5] Wang W, Zhang X S, Li M. A filled function method dominated by filter for nonlinearly global optimization[J]. J. Appl. Math., 2015, 8(3):8–18.
[6] Wu C Z, Kok L T, Volker R. A filled function method for optimal discrete-valued control problems[J]. Glob. Optim., 2009, 44(2):213–225.
[7] Fletcher R, Leyffer S. Nonlinear programming without a penalty function[J]. Math. Prog., 2002,91(2):239–269.
[8] Fletcher R, Leyffer S, Toint P L. On the global convergence of a filter-SQP algorithm[J]. Siam J.Optim., 2006, 13(1):44–59.
[9] Michael U, Stefan U, Luis N V. A globally convergent primal-dual interior-point filter method for nonlinear programming[J]. Math. Prog., 2004, 100(2):379–410.
[10] Andreas W, Lorenz T B. Line search filter methods for nonlinea programming:local convergence[J].SIAM J. Optim., 2005, 16(2):1–31.
[11]胡铨,王薇.求解带箱式约束全局优化问题的滤子填充函数方法[J].运筹学学报, 2016, 03:57–67.
[12] Rosen J B. The gradient projection method for nonlinear programming, Part I. linear constraints[J]. SIAM, 1960, 8(1):181–217.
[13] Zhang X S. On the convergence of Rosen’s gradient projection method:three-dimension case[J].Acta Math. Appl. Sin., Engl. Ser., 1987, 3(3):280–288.
[14] Du D. Remarks on the convergence of Rosen’s gradient projection method[J]. Acta Math. Appl.Sin., Engl. Ser., 1987, 3(3):270–279.
[15] Wang W, Hua S L, Tang J J. A generalized gradient projection filter algorithm for inequality constrained optimization[J]. J. Appl. Math., 2013, 2013(2):4819–4828.
[16] Gao J, Wang W. A generalized gradient projection filter method for arbitrary initial point[J]. Oper.Res. Trans., 2013, 17(2):124–130.