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 - <p style="text-align: justify;">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&#39;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.</p>