Abstract
Our aim in this paper is to present sufficient conditions for error bounds in terms of Fréchet and limiting Fréchet subdifferentials in general Banach 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 of imposing conditions either on C or D. We use these results to prove the nonemptiness and weak-star compactness of Fritz–John and Karush–Kuhn–Tucker multiplier sets, to establish the 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.
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Bosch, P., Jourani, A. & Henrion, R. Sufficient Conditions for Error Bounds and Applications. Appl Math Optim 50, 161–181 (2004). https://doi.org/10.1007/s00245-004-0799-5
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DOI: https://doi.org/10.1007/s00245-004-0799-5