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Volume 38, Issue 3
A Stochastic Moving Balls Approximation Method over a Smooth Inequality Constraint

Leiwu Zhang

DOI: 10.4208/jcm.1912-m2016-0634

J. Comp. Math., 38 (2020), pp. 528-546.

Published online: 2020-03

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  • 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.

  • Keywords

Smooth convex constrained minimization, Large scale problem, Moving Balls Approximation, Regularized logistic regression.

  • AMS Subject Headings

65C20, 90C15, 90C25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zaleiwu@sina.com (Leiwu Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-528, author = {Zhang , Leiwu}, title = {A Stochastic Moving Balls Approximation Method over a Smooth Inequality Constraint}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1912-m2016-0634}, url = {http://global-sci.org/intro/article_detail/jcm/15799.html} }
TY - JOUR T1 - A Stochastic Moving Balls Approximation Method over a Smooth Inequality Constraint AU - Zhang , Leiwu JO - Journal of Computational Mathematics VL - 3 SP - 528 EP - 546 PY - 2020 DA - 2020/03 SN - 38 DO - http://doi.org/10.4208/jcm.1912-m2016-0634 UR - https://global-sci.org/intro/article_detail/jcm/15799.html KW - Smooth convex constrained minimization, Large scale problem, Moving Balls Approximation, Regularized logistic regression. AB -

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.

Zhang , Leiwu. (2020). A Stochastic Moving Balls Approximation Method over a Smooth Inequality Constraint. Journal of Computational Mathematics. 38 (3). 528-546. doi:10.4208/jcm.1912-m2016-0634
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