Relaxation methods for problems with strictly convex separable costs and linear constraints

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32 Scopus citations

Abstract

We consider the minimization problem with strictly convex, possibly nondifferentiable, separable cost and linear constraints. The dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution by parallel methods based on Gauss-Seidel relaxation. We show that these methods yield the optimal primal solution and, under additional assumptions, an optimal dual solution. To do this it is necessary to extend the classical Gauss-Seidel convergence results because the dual cost may not be strictly convex, and may have unbounded level sets.

Original languageEnglish (US)
Pages (from-to)303-321
Number of pages19
JournalMathematical Programming
Volume38
Issue number3
DOIs
StatePublished - Oct 1987
Externally publishedYes

Keywords

  • Fenchel duality
  • Gauss-Seidel relaxation
  • strict convexity
  • strong convexity

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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