On the convergence of asynchronous parallel algorithm for large-scale linearly constrained minimization problem |
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Authors: | Congying Han Yongli Wang |
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Affiliation: | School of Information Science and Engineering, Shandong University of Science and Technology, No. 579 of Qian WanGang Road, Qingdao, Shandong Province 266510, China |
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Abstract: | As a synchronization parallel framework, the parallel variable transformation (PVT) algorithm is effective to solve unconstrained optimization problems. In this paper, based on the idea that a constrained optimization problem is equivalent to a differentiable unconstrained optimization problem by introducing the Fischer Function, we propose an asynchronous PVT algorithm for solving large-scale linearly constrained convex minimization problems. This new algorithm can terminate when some processor satisfies terminal condition without waiting for other processors. Meanwhile, it can enhances practical efficiency for large-scale optimization problem. Global convergence of the new algorithm is established under suitable assumptions. And in particular, the linear rate of convergence does not depend on the number of processors. |
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Keywords: | Parallel algorithm Constrained convex optimization Nonlinear programming Large-scale minimization |
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