Metodi di ottimizzazione non vincolata, L. Grippo, M. Sciandrone, Springer-Verlag, 2011
Additional Lecture Notes
Learning Objectives
To understand optimality condition and to be able to use them. Knowledge of main algorithmic approaches for local optimization and their theoretical and computational aspects
Prerequisites
Elementary knowledge of calculus (Taylor expansions, gradients, Hessian matrix)
Linear algebra
A course on operations Research / linear programming might prove useful
Teaching Methods
Front lectures. Lectures are video recorded and made availavable through Moodle
Type of Assessment
Written or oral exam on all the course subjects
The exam consists in checking, through theooretical questions:
- knowledge of tthe theory of optimization (optimality conditions)
- knowledge of optimization applied to machine learning
- knowledge of non linear optimization algorithms
Course program
Introduction; optimization models and examples
Basic definitions
Optimality conditions for constrained optimization (KKT conditions)
Introduction to machine learning
Convergence of algorithms
One-dimensional optimization
Gradient descent methods
Newton methods
Conjugate direction methods
Quasi-Newton methods
Trust Region methods
Constrained optimization methods