EXTENDED REAL-VALUED FUNCTIONS- A UNIFIED APPROACH

Abstract

Extended real-valued functions are often used in optimization theory, but in different ways for in- fimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and into which one results of convex analysis can be embedded. Our approach preserves continuity and the Chebyshev norm when extending a func- tional to the entire space. The basic idea also works for other spaces than the extended set of real numbers. Moreover, we characterize semicontinuity, convexity, linearity and related properties of extended real-valued functions