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Homogeneous approximations of functions sets and mappings
Dini and Hadamard derivatives
28 other sections not shown
akgk Assume called Clarke subdifferential coincides concave concave function cone continuously codifferentiable Convex Analysis convex compact sets convex function convex set daf(x definition denote descent direction dh(x Dini derivative direction g directional derivative directionally differentiable element equality equivalent Example exists function f gradient Hadamard differentiable Hence holds implicit function implies inclusion inequality Lemma Let a function let us consider Let us show liminf limsup Lipschitz function locally Lipschitz lower semicontinuous mapping H maximum minimal minimum point Minkowski duality multi-valued mapping neighbourhood nonempty open set X C operation Optimization point x point x0 positively homogeneous problem Proof properties Proposition quasidifferentiable functions real number regularity condition relation Remark satisfied Section sequence set ft sets df(x space steepest descent steepest descent direction subdifferential mapping sublinear function Subsection sufficiently small superdifferential superlinear support function Theorem 3.1 twice continuously uniformly upper semicontinuous vector yields zero