Abstract

Let X be a real normed linear space, f, fⁿ, n ∈ ℕ, be extended real-valued proper closed convex functions on X. A sequence {xₙ} in X is called diagonally stationary for {fⁿ} if for all n there exists xn⋆∈∂fn(xn)x_n^\star \in \partial f^n(x_n) such that ∥xn⋆∥⋆→0\|x_n^\star\|_\star \to 0. Such sequences arise in approximation methods for the problem of minimizing f. We present some general quantitative convergence results based upon metric variational convergence theory, appropriate equi-well-posedness and conditioning concepts for the limit function f, and Fejér monotonicity.

Author information

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B. Lemaire

Université Montpellier II, Place E. Bataillon, F-34095 Montpellier Cedex 5

Keywords

  • Asymptotical behaviour
  • conditioning
  • convex optimization
  • diagonal stationarity
  • error estimate
  • Fejér monotonicity
  • variational convergence
  • well-posedness

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Suggested citation

B. Lemaire. “Bounded Diagonally Stationary Sequences in Convex Optimization.” Journal of Convex Analysis 1 (1994), No. 1, 75–86. https://doi.org/10.68381/jca01005

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press LLC.