WIAS Preprint No. 679, (2001)

Error bounds and their application



Authors

  • Bosch, Paul
  • Jourani, Abderrahim
  • Henrion, René

2010 Mathematics Subject Classification

  • 90C31 49J52

Keywords

  • Error Bounds, Approximate Subdifferential, Sensitivity Analysis, Local Controllability Error Bounds, Local Controllability

Abstract

Our aim in this paper is to present sufficient conditions for error bounds in terms of Frechet and limiting Frechet subdifferentials outside of Asplund spaces. This allows us to develop sufficient conditions in terms of the approximate subdifferential for systems of the form (𝑥, 𝑦) ∈ 𝐶 × 𝐷, 𝑔(𝑥, 𝑦, 𝑢) = 0, where 𝑔 takes values in an infinite dimensional space and 𝑢 plays the role of a parameter. This symmetric structure offers us the choice to impose condtions either on 𝐶 or 𝐷. We use these results to prove nonemptyness and weak-star compactness of Fritz-John and Karuch-Kuhn-Tucker multiplier sets, to establish Lipschitz continuity of the value function and to compute its subdifferential and finally to obtain results on local controllability in control problems of nonconvex unbounded differential inclusions.

Appeared in

  • Applied Mathematics and Optimization 50 (2004), pp. 161-181 under the new title: Sufficient Conditions for Error Bounds and Applications.

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