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| Paper IPM / M / 16469 |
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| Abstract: | |
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In this paper, we introduce the notions of global subdifferentials associated to the global directional derivatives. We provide the usual properties, calculus rules and comparisons with other well-known subdifferentials as Fr´ echet and Dini subdifferentials. Furthermore, we prove that the lower global subdifferential is an abstract subdifferential, that is, the lower global subdifferential satisfies the standar properties of the subdifferential operators. Finally, two applications in nonconvex nonsmooth optimization are provided: necessary and sufficient optimality conditions for a point to be local minima, and a revisited characterization for nonsmooth quasiconvex functions.
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