The course will provide an up-to-date introduction to modern optimization algorithms.

The advances in computer technology have promoted the field of nonlinear optimization, which has become today an essential tool to solve intelligently complex scientific and engineering problems.

Smooth Unconstrained Optimization: Classical algorithms and methods of analysis. Descent methods. Line search techniques. Newton's type methods, Conjugate Gradients. Rate of convergence Analysis.

First Order Methods for Huge Scale Convex Problems: Gradient/Subgradient, Fast Proximal-Gradient Schemes, Complexity Analysis, Smoothing methods. 
Lagrangian methods for convex optimization:  Decomposition splitting schemes for large scale problems: augmented Lagrangians, alternating direction of multiplier methods, nonquadratic proximal schemes. 
Self-Concordance Theory and Complexity Analysis: Self-concordant functions. Polynomial Interior Point Algorithms. Newton's Method Revisited. 
Semidefinite and Conic Programming : Theory, polynomial algorithms, and applications to combinatorial optimization problems and engineering.
Modern Applications in Science and Engineering:  Throughout the course, we will discuss several prototype optimization models and relevant algorithms studied in the course toward tefficient solution of problems in various applied areas: Signal Processing, Machine Learning, Sensor Networks Localization problems, etc...