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2007•Optimization methods & softwareRequires access

A merit function approach to the subgradient method with averaging

Andrzej Ruszczyński

Open publisher page 14 citations

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.

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What this paper is about

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.

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OpenAlex reports 14 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Subgradient method, Mathematical optimization, Convergence (economics), Mathematics, Regular polygon, Convex optimization, Dual (grammatical number), Convex function

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