Boyd S., Vandenberghe L. Convex Optimization 2009 + Sol. Man.

Textbook in PDF format

This book is about convex optimization, a special class of mathematical optimization
problems, which includes least-squares and linear programming problems. It
is well known that least-squares and linear programming problems have a fairly
complete theory, arise in a variety of applications, and can be solved numerically
very efficiently. The basic point of this book is that the same can be said for the
larger class of convex optimization problems.
Our main goal is to help the reader develop a working knowledge of
convex optimization, i.e., to develop the skills and background needed
to recognize, formulate, and solve convex optimization problems.
Theory
Convex sets
Convex functions
Convex optimization problems
Duality
Applications
Approximation and fitting
Statistical estimation
Geometric problems
Algorithms
Unconstrained minimization
Equality constrained minimization
Interior-point methods
Appendices
Mathematical background
Problems involving two quadratic functions
Numerical linear algebra background