A comprehensive introduction to convexity and optimization in Rn This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material. Convexity and Optimization in Rn provides detailed discussion of: *Requisite topics in real analysis *Convex sets *Convex functions *Optimization problems *Convex programming and duality *The simplex method A detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively class-tested notes.