Browsing by Author "Gidey, Gebretsadik"

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    Di_erence of Convex(D.C.) Functions and Their Minimal Representations
    (Addis Ababa University, 2013-06-27) Gidey, Gebretsadik; Mitiku, Semu(PhD)
    A function f de_ned on a given convex set X which can be expressed as a di_erence of two convex (continuous) functions is called d.c function or _-convex function. The functions which are Lipschitz and bounded variation are expressible as a d.c. function and since those family of d.c. functions form a linear space as well as a lattice, it admits many operations. The decomposition of a given function f as a d.c. functions is not unique. Choosing the better (minimal) decomposition is useful in describing the optimality conditions for d.c. optimization