求解非线性方程组的锥模型信赖域算法
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摘要
针对传统信赖域算法计算复杂、难度较大等问题,提出一种基于非单调的锥模型信赖域算法.引入松弛变量将非线性系统问题转换为带非负约束的非线性最优问题,借助KKT条件以及NCP函数,每次迭代时求解一个线性方程组,通过一阶、二阶结合,扩大了锥模型信赖域半径,加大信赖域迭代步,提高了收敛速度.信赖域算法具有整体收敛性.
Aiming at the complexity and difficulty of traditional trust region algorithm,this paper proposed a trust region algorithm based on non-monotonic cone model,by introducing relaxation variables,transformed the problem of nonlinear systems into a non-linear optimal problem with non-negative constraints,with the help of KKT condition and NCP function,solved a system of linear equations at each iteration,by means of combining first-order and second-order,broadened the trust region radius of cone model,enlarged the iteration step of trust region,increased the convergence rate. The trust region algorithm has global convergence.
Aiming at the complexity and difficulty of traditional trust region algorithm,this paper proposed a trust region algorithm based on non-monotonic cone model,by introducing relaxation variables,transformed the problem of nonlinear systems into a non-linear optimal problem with non-negative constraints,with the help of KKT condition and NCP function,solved a system of linear equations at each iteration,by means of combining first-order and second-order,broadened the trust region radius of cone model,enlarged the iteration step of trust region,increased the convergence rate. The trust region algorithm has global convergence.
引文
[1]王晗,徐潇源,严正.基于改进信赖域算法的孤岛交直流混合微电网潮流计算[J].电力系统自动化,2017,41(20):38-46.
[2]周群艳.基于线性模型的自适应信赖域方法[J].运筹与管理,2016,25(4):87-92.
[3]唐江花.求解非线性方程组的新的信赖域方法[J].聊城大学学报:自然科学版,2017,30(1):38-43.
[4]王鹏,朱德通.一个解界约束非线性方程组的无导数回溯线搜索仿射内点信赖域方法[J].系统科学与数学,2017,37(1):155-171.
[5]周群艳.基于线性模型的自适应信赖域方法[J].运筹与管理,2016,25(4):87-92.
[6]潘克家,汤井田,杜华坤,等.轴对称地层中高分辨率阵列侧向测井信赖域反演法[J].地球物理学报,2016,59(8):3 110-3 120.
[2]周群艳.基于线性模型的自适应信赖域方法[J].运筹与管理,2016,25(4):87-92.
[3]唐江花.求解非线性方程组的新的信赖域方法[J].聊城大学学报:自然科学版,2017,30(1):38-43.
[4]王鹏,朱德通.一个解界约束非线性方程组的无导数回溯线搜索仿射内点信赖域方法[J].系统科学与数学,2017,37(1):155-171.
[5]周群艳.基于线性模型的自适应信赖域方法[J].运筹与管理,2016,25(4):87-92.
[6]潘克家,汤井田,杜华坤,等.轴对称地层中高分辨率阵列侧向测井信赖域反演法[J].地球物理学报,2016,59(8):3 110-3 120.