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.
