Calafiore G.C., El Ghaoui L. Optimization Models

Cambridge: Cambridge University Press, 2014. — 648 p.Several textbooks have appeared in recent years, in response to the growing needs of the scientific community in the area of convex optimization. Most of these textbooks are graduate-level, and indeed contain a good wealth of sophisticated material. Our treatment includes the following distinguishing elements.
The book can be used both in undergraduate courses on linear algebra and optimization, and in graduate-level introductory courses on convex modeling and optimization.
The book focuses on modeling practical problems in a suitable optimization format, rather than on algorithms for solving mathematical optimization problems; algorithms are circumscribed to two chapters, one devoted to basic matrix computations, and the other to convex optimization.
About a third of the book is devoted to a self-contained treatment of the essential topic of linear algebra and its applications.
The book includes many real-world examples, and several chapters devoted to practical applications.
We do not emphasize general non-convex models, but we do illustrate how convex models can be helpful in solving some specific non-convex ones.Motivating examples
Optimization problems
Important classes of optimization problems
History
Linear algebra models
Vector basics
Norms and inner products
Projections onto subspaces
Functions
Exercises
Matrix basics
Matrices as linear maps
Determinants, eigenvalues, and eigenvectors
Matrices with special structure and properties
Matrix factorizations
Matrix norms
Matrix functions
Exercises
Basics
The spectral theorem
Spectral decomposition and optimization
Positive semidefinite matrices
Exercises
Singular value decomposition
Matrix properties via SVD
SVD and optimization
Exercises
Motivation and examples
The set of solutions of linear equations
Least-squares and minimum-norm solutions
Solving systems of linear equations and LS problems
Sensitivity of solutions
Direct and inverse mapping of a unit ball
Variants of the least-squares problem
Exercises
Computing eigenvalues and eigenvectors
Solving square systems of linear equations
QR factorization
Exercises
Convex optimization models
Convex sets
Convex functions
Convex problems
Optimality conditions
Duality
Exercises
Linear, quadratic, and geometric models
Unconstrained minimization of quadratic functions
Geometry of linear and convex quadratic inequalities
Linear programs
Quadratic programs
Modeling with LP and QP
LS-related quadratic programs
Geometric programs
Exercises
Second-order cone programs
SOCP-representable problems and examples
Robust optimization models
Exercises
From linear to conic models
Linear matrix inequalities
Semidefinite programs
Examples of SDP models
Exercises
Introduction to algorithms
Technical preliminaries
Algorithms for smooth unconstrained minimization
Algorithms for smooth convex constrained minimization
Algorithms for non-smooth convex optimization
Coordinate descent methods
Decentralized optimization methods
Exercises
Applications
Overview of supervised learning
Least-squares prediction via a polynomial model
Binary classification
A generic supervised learning problem
Unsupervised learning
Exercises
Single-period portfolio optimization
Robust portfolio optimization
Multi-period portfolio allocation
Sparse index tracking
Exercises
Control problems
Continuous and discrete time models
Optimization-based control synthesis
Optimization for analysis and controller design
Exercises
Digital filter design
Antenna array design
Digital circuit design
Aircraft design
Supply chain management
Exercises