Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem

In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computat...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 30; no. 3; pp. 707 - 720
Main Authors Han, Cong-ying, Zheng, Fang-ying, Guo, Tian-de, He, Guo-ping
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2014
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
全局收敛性
坐标旋转
并行算法
并行计算
最小化问题
梯度函数
线性约束优化
非线性规划
large-scale minimization
constrained convex optimization
90C30
90C52
nonlinear programming
parallel algorithm
90C06
49M37
65Y05
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Summary:In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.
Bibliography:In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.
11-2041/O1
nonlinear programming; large-scale minimization; parallel algorithm; constrained convex opti-mization
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-013-0300-9