an:03950216
Zbl 0591.90073
Hiriart-Urruty, J.-B.
Generalized differentiability, duality and optimization for problems dealing with differences of convex functions
EN
Convexity and duality in optimization, Proc. Symp., Groningen/Neth. 1984, Lect. Notes Econ. Math. Syst. 256, 37-70 (1985).
1985
a
90C30 49M37 26B05 26B25 90-02 49N15
generalized differentiability; d.c. functions; difference of two convex functions; survey; differential properties; locally Lipschitz functions; duality results
[For the entire collection see Zbl 0569.00010.]
A large number of optimization problems of practical interest actually involve d.c. functions, i.e. functions that can be expressed as a difference of two convex functions. From a theoretical point of view, the importance of such functions stems from their relationship to convex functions and the fact that they constitute a linear space which is a dense subset of the space of continuous functions over a compact set. The reviewed article gives an excellent survey of the main known results on the analysis and optimization of d.c. functions. The following questions are discussed: differential properties, characterization of d.c. functions among locally Lipschitz functions, finding the ''best'' d.c. representation of a given function, duality results, in particular the basic Toland's duality relation. Also a preview on procedures for globally minimizing a d.c. function is presented.
Hoang Tuy
Zbl 0569.00010