Dual representations of classes of positively homogeneous functions. (English) Zbl 0997.90098

Demyanov, V. (ed.) et al., Quasidifferentiability and related topics. Dedicated to Prof. Franco Giannessi on his 65th birthday and to Prof. Diethard Pallaschke on his 60th birthday. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 43, 73-84 (2000).
It is shown that a dual characterization exists for a large class of positively homogeneous functions. By means of the related representation, where MSL (minimum of sublinear) functions and exhausters are involved, theorems of the alternative are deduced. Generalizations of the well-known theorems of Farkas and of Gordon are playing a key position in the investigations. The derived theorems can finally be used to formulate necessary conditions for optimality problems with inequality constraints of a very general type.
For the entire collection see [Zbl 0949.00047].


90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)