On the convergence of asynchronous parallel algorithm for large-scale linearly constrained minimization problem

• Published in: Applied mathematics and computation Vol. 211; no. 2; pp. 434 - 441
• Main Authors: Han, Congying, Wang, Yongli, He, Guoping
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.05.2009; Elsevier
• Subjects: Acceleration of convergence; Constrained convex optimization; Exact sciences and technology; Large-scale minimization; Mathematical analysis; Mathematics; Nonlinear programming; Numerical analysis; Numerical analysis. Scientific computation; Parallel algorithm; Sciences and techniques of general use; Constrained convex optimization; Parallel algorithm; Nonlinear programming; Large-scale minimization; Unconstrained optimization; Convergence acceleration; Optimization method; Non linear programming; Synchronization; Convergence; Constrained optimization; Numerical analysis; Algorithm performance; Applied mathematics; Convergence rate
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.01.081

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.