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


49K10 Optimality conditions for free problems in two or more independent variables
26B05 Continuity and differentiation questions
49J52 Nonsmooth analysis
90C30 Nonlinear programming


Zbl 0538.49020
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