Mathematical Programming

, Volume 120, Issue 1, pp 27–48 | Cite as

Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities

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Abstract

We study subgradient projection type methods for solving non-differentiable convex minimization problems and monotone variational inequalities. The methods can be viewed as a natural extension of subgradient projection type algorithms, and are based on using non-Euclidean projection-like maps, which generate interior trajectories. The resulting algorithms are easy to implement and rely on a single projection per iteration. We prove several convergence results and establish rate of convergence estimates under various and mild assumptions on the problem’s data and the corresponding step-sizes.

Keywords

Non-differentiable convex optimization Variational inequalities Ergodic convergence Subgradient methods Interior projection-like maps 

Mathematics Subject Classification (2000)

90C25 90C33 65K05 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institut Camille JordanUniversity of Lyon ILyonFrance
  2. 2.School of Mathematical SciencesTel-Aviv UniversityRamat-AvivIsrael

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