Basic Concepts of Global Optimization

Abstract

This chapter introduces the reader to the basic concepts that form the foundation for the global optimization theoretical developments, methods and applications. In section 2.1 the fundamentals of convex sets are discussed. In section 2.2 the subject of convex and concave functions is presented. In section 2.3 the definitions and properties of quasiconvex and pseudoconvex functions are discussed. Section 2.4 presents the definition and properties of the convex envelopes. Section 2.5 presents the definitions of the local, global optima and E-global optima. Finally, section 2.6 introduces the reader to the basics of difference of convex functions denoted as D.C. functions.