A merit function approach to the subgradient method with averaging

Authors:
Andrzej Ruszczynski
Affiliations:
Department of Management Science and Information Systems, Rutgers University, Piscataway, New Jersey, USA
Venue:
Optimization Methods & Software
Year:
2008

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Abstract

We consider a version of the subgradient method for convex nonsmooth optimization involving subgradient averaging. Using a merit function approach in the space of decisions and subgradient estimates, we prove convergence of the primal variables to an optimal solution and of the dual variables to an optimal subgradient. Application to dual convex optimization problems is discussed.