Some sufficient optimality conditions in nonsmooth analysis

This paper covers three different kinds of second-order sufficient conditions for identifying a strict local minimum of an extended-real-valued function. The different sufficient conditions are based on different second-order subdifferentials: the second-order lower Dini-directional derivative, and two different generalized derivatives (the graphical derivative and the coderivative) of the proximal subdifferential. The authors develop sufficient conditions of two kinds, based on the two generalized derivatives, and demonstrate when these conditions are implied by a sufficient condition based on the Dini-directional derivative. All three kinds of sufficient conditions are equivalent for infimal convolutions of lowersemicontinuous, prox-bounded functions.