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Throughout, X stands for a real Banach space, S X for its unit sphere, X * for its to-pological dual, and ·, ·· for the duality pairing. All the functions f : X → R ∪ {+∞} are lower semicontinuous. The Clarke subdifferential , the Hadamard subdifferential and the Fréchet subdifferential of f are respectively denoted by ∂ C f , ∂ H f and ∂ F f. The Zagrodny(More)
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