Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces

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On optimal control of a sweeping process coupled with an ordinary differential equation (2014, background): “Indeed, when dealing with a differential inclusion, the right–hand side is usually required to be Lipschitz continuous, such as in [8] or [28] or this requirement is somehow relaxed, such as the one–sided Lipschitzian property from [13].”
OPTIMAL CONTROL OF THE SWEEPING PROCESS (2012, background): “To the best of our knowledge, the strong approximation type obtained for general differential inclusions (see [5, 11, 13] and the references therein) cannot be applied to the sweeping system under consideration since the Lipschitz continuity assumption of [11, 13] and the “modified one-sided Lipschi”