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Necessary and sufficient conditions for isolated local minima of nonsmooth functions. (English) Zbl 0604.49017
In a recent paper, A. Auslender [ibid. 22, 239-254 (1984; Zbl 0538.49020)] derived conditions for isolated local minima of order 1 and 2 in finite dimensional minimization problems with locally Lipschitzian objective functions and closed feasibility sets. In the paper under review, Auslender’s results are generalized to problems with arbitrary extended-real-valued functions and to isolated minima of arbitrary order. The conditions are stated in terms of lower and upper Dini directional derivatives and their higher order analogues.
Reviewer: M.Vlach

MSC:
49K10Free problems in several independent variables (optimality conditions)
26B05Continuity and differentiation questions (several real variables)
49J52Nonsmooth analysis (other weak concepts of optimality)
90C30Nonlinear programming