Linear Subspaces and Affine Manifolds

Abstract

The first three chapters of this book discuss the concept of linear subspaces and some of its important subsets — namely, affine manifolds, convex cones and sets. The notion of convexity plays a dominant role in nonlinear programming and is explored in depth in these chapters. Chapter 4 deals with convex and convex-like functions. As we will see later, certain convex sets can be associated with each of these functions. The important results of these chapters are used later to develop optimality conditions for nonlinear programs. The chapters also do contain several other related results which have been used elsewhere in the study of nonlinear programs or, in the opinion of the authors, are likely to be useful in advanced work in this area.