An Easy Path to Convex Analysis and Applications

This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location. In addition, this book: - Explains the fundamental theory with an accessible and understandable variational geometric approach; - Provides easy access to theoretical and numerical applications to convex optimization and geometry; - Simplifies relative interiors of convex sets in developing the theory of generalized differentiation in finite dimensions.