Dierence Of Convex(d.c.) Functions And Their Minimal Representations

A function f de_ned on a given convex set X which can be expressed as a di_erencernof two convex (continuous) functions is called d.c function or _-convex function. Thernfunctions which are Lipschitz and bounded variation are expressible as a d.c. functionrnand since those family of d.c. functions form a linear space as well as a lattice, it admitsrnmany operations.rnThe decomposition of a given function f as a d.c. functions is not unique. Choosingrnthe better (minimal) decomposition is useful in describing the optimality conditions forrnd.c. optimization

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