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Parallel algorithms for large-scale linearly constrained minimization problem
Authors:Cong-ying Han  Fang-ying Zheng  Tian-de Guo  Guo-ping He
Affiliation:1. School of Mathematical Sciences, University of the Chinese Academy of Sciences, No.19(A), Yuquan Road, Shijingshan District, Beijing, 100049, China
2. Department of Mathematical Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China
3. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, 266510, China
Abstract: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.
Keywords:nonlinear programming  large-scale minimization  parallel algorithm  constrained convex opti-mization
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