This extensive rigorous textbook, developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization.

The author's guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class.

web.stanford.edu/~boyd/cvxbook/
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. [...] The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them.