IIASA RepositoryA directional implicit function theorem for quasidifferentiable functionsV. A.DemidovaauthorV.F.DemyanovauthorThe implicit and inverse function theorems provide an essential component of classical differential calculus, and for this reason many attempts have been made to extend these theorems to nonsmooth analysis (see, for example, the work of F. Clarke, H. Halkin, J.-B. Hiriart-Urruty, A.D. Ioffe, B.H. Pourciau, J. Warga). In this paper, we consider the case of quasidifferentiable functions. It is shown that to obtain nontrivial results it is necessary to study a directional implicit function problem (it turns out that in some directions there are several functions, while in others there are none).1986Springer Berlin HeidelbergBook Section

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