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Quasidifferential calculus and first-order optimality conditions in nonsmooth optimization. (English) Zbl 0604.49012
This paper is concerned with first-order optimality conditions for nonsmooth extremal problems. The author first studies positively homogeneous functions (differences of sublinear functions) which are used later in local approximations and difference convex domains. A theorem stating a necessary and sufficient condition for a positively homogeneous function $$\phi$$ to belong to the linear space of difference sublinear functions on $$E_ n$$ is proved. Furthermore it is proved that every closed cone C is associated with a difference sublinear function $$\phi$$ such that $$C=\{x| \phi (x)\leq 0\}$$. After some further remarks on quasidifferentiable functions and approximations using difference sublinear functions the last section concerns first-order optimality conditions and the theory of quasidifferential calculus developed earlier.
Reviewer: G.van der Hoek

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