A Stochastic Moving Balls Approximation Method over a Smooth Inequality Constraint (Journal of Computational Mathematics, 2020)
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 stochasticMoving Balls Approximation (SMBA) method. Like stochastic gradient (SG) methods, theSMBA method's iteration cost is independent of the number of component functions andby exploiting the smoothness of the constraint function, our method can be easily implemented. Theoretical and computational properties of SMBA are studied, and convergenceresults are established. Numerical experiments indicate that our algorithm dramaticallyoutperforms the existing Moving Balls Approximation algorithm (MBA) for the structureof our problem.
Keywords: Smooth convex constrained minimization; Large scale problem; Moving Balls Approximation; Regularized logistic regression.