Incrementally Updated Gradient Methods for Constrained and Regularized Optimization

Paul Tseng and Sangwoon Yun ()
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Paul Tseng: University of Washington
Sangwoon Yun: Sungkyunkwan University

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 3, No 7, 832-853

Abstract: Abstract We consider incrementally updated gradient methods for minimizing the sum of smooth functions and a convex function. This method can use a (sufficiently small) constant stepsize or, more practically, an adaptive stepsize that is decreased whenever sufficient progress is not made. We show that if the gradients of the smooth functions are Lipschitz continuous on the space of n-dimensional real column vectors or the gradients of the smooth functions are bounded and Lipschitz continuous over a certain level set and the convex function is Lipschitz continuous on its domain, then every cluster point of the iterates generated by the method is a stationary point. If in addition a local Lipschitz error bound assumption holds, then the method is linearly convergent.

Keywords: Incrementally updated gradient method; Linear convergence; Error bound; Backpropagation; Neural network training; Regularization (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0409-2

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