Abstract
This chapter discusses convex sets and convex functions. The notion of extreme point of a convex set plays an important role in mathematical programming, especially in linear programming. A closed bounded convex set S—a subset of IRn—is the convex hull of its extreme points. A set in IRn, which is given by the intersection of a finite number of closed half spaces in IRn, is called a convex polyhedron or polyhedral set. The term “convex” is superfluous as it follows from convexity of the half spaces that polyhedral are (closed) convex sets. Convex functions (and their generalizations) also play a central role in the analysis of extremum problems. The importance of convex functions in problems of this kind lies mainly in some basic properties, as described in the chapter.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Mathematics of Optimization: Smooth and Nonsmooth Case
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
