Modified Spectral Projected Subgradient Method: Convergence Analysis and Momentum Parameter Heuristics
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2016, Vol 4, Issue 2
Abstract
The Modified Spectral Projected Subgradient (MSPS) was proposed to solve Langrangen Dual Problems, and its convergence was shown when the momentum term was zero. The MSPS uses a momentum term in order to speed up its convergence. The momentum term is built on the multiplication of a momentum parameter and the direction of the previous iterate. In this work, we show convergence when the momentum parameter is a non-zero constant. We also propose heuristics to choose the momentum parameter intended to avoid the Zigzagging Phenomenon of Kind I. This phenomenon is present in the $MSPS$ when at an iterate the subgradient forms an obtuse angle with the previous direction. We identify and diminish the Zigzagging Phenomenon of Kind I on Setcovering problems, and compare our numerical results to those of the original MSPS algorithm.
Authors and Affiliations
Milagros Loreto, Samantha Clapp, Charles Cratty, Breeanna Page
Keywords
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