Mathematical Programming

, Volume 62, Issue 1, pp 261-275

First online:

Convergence of some algorithms for convex minimization

  • Rafael CorreaAffiliated withDepartamento de Matematicas, Universidad de Chile
  • , Claude LemaréchalAffiliated withDomaine de Voluceau-Rocquencourt, INRIA

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We present a simple and unified technique to establish convergence of various minimization methods. These contain the (conceptual) proximal point method, as well as implementable forms such as bundle algorithms, including the classical subgradient relaxation algorithm with divergent series.

AMS Subject Classification

65K05 90C25

Key words

Nondifferentiable optimization convex programming proximal point method bundle algorithms global convergence