Berkovitz L. Convexity and Optimization in Rn 2001

Textbook in PDF format

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