zbMATH — the first resource for mathematics

Exhaustive families of approximations revisited. (English) Zbl 1043.49021
Gilbert, Robert P. (ed.) et al., From Convexity to nonconvexity. Dedicated to the memory of Gaetano Fichera. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-7144-5/hbk). Nonconvex Optim. Appl. 55, 43-50 (2001).
Summary: The notions of exhaustive families of upper convex and lower concave approximations (in the sense of B. N. Pschenichnyj) were introduced in 1982. For some classes of nonsmooth functions, these tools appeared to be very productive and constructive (e.g., in the case of quasidifferentiable functions). In the present paper we introduce notions of upper exhauster and lower exhauster. It is demonstrated how to employ these notions to describe necessary optimality conditions and to find directions of steepest ascent and descent. If a proper exhauster is known, the above problems are reduced to the problems of finding the nearest points to convex sets.
For the entire collection see [Zbl 0972.00025].

49J52 Nonsmooth analysis
90C46 Optimality conditions and duality in mathematical programming