Year: 2020
Author: Leiwu Zhang
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 528–546
Abstract
We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint. We propose and analyze a stochastic Moving Balls Approximation (SMBA) method. Like stochastic gradient (SG) methods, the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function, our method can be easily implemented. Theoretical and computational properties of SMBA are studied, and convergence results are established. Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm (MBA) for the structure of our problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1912-m2016-0634
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 528–546
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Smooth convex constrained minimization Large scale problem Moving Balls Approximation Regularized logistic regression.