ISSN:
1572-932X
Keywords:
Primary: 58C20
;
Secondary: 49J52, 90C30, 58C06, 46G05, 26E15
;
Nonsmooth analysis
;
parabolic epiderivative
;
second-order tangent set
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, a calculus for two second-order directional derivatives is presented and then applied in the development of second-order necessary optimality conditions for a nonsmooth mathematical program. The formulae of this calculus, which include rules for sums, pointwise maxima, and certain compositions of functions, are valid for a large class of non-Lipschitzian functions and in fact subsume the sharpest results of the calculus of first-order upper and lower epiderivatives. Two methods are utilized in the derivation of these formulae. One centers around the concept of metric regularity, while the other relies upon the use of recession cones and ‘interior tangent sets’.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01027635
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