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- W2015241497 abstract "We establish a general Fermat rule for the problem of minimizing a lower semicontinuous function on a convex subset of a Banach space. Our basic tool is a constrained variational principle derived from the smooth variational principle of Borwein and Preiss. Specializing the Fermat rule to the case when the convex set is a drop, we obtain a multidirectional Rolle-type inequality from which, in turn, we deduce a multidirectional mean value inequality, in the line of Clarke and Ledyaev. We follow the abstract approach of our previous paper [Trans. Amer. Math. Soc., 347 (1995), pp. 4147--4161], thus covering all standard situations met in applications, while stressing the links between the results and the few key properties that are needed." @default.
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- W2015241497 title "Nonsmooth Constrained Optimization and Multidirectional Mean Value Inequalities" @default.
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- W2015241497 doi "https://doi.org/10.1137/s105262349732339x" @default.
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