Abstract
It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given bounded level set.
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This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, US Department of Energy, under Contract W-31-109-Eng-38.
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Griewank, A., Jongen, H.T. & Kwong, M.K. The equivalence of strict convexity and injectivity of the gradient in bounded level sets. Mathematical Programming 51, 273–278 (1991). https://doi.org/10.1007/BF01586939
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DOI: https://doi.org/10.1007/BF01586939