Optimality Conditions
Local unconstrained optimization
Local Constrained Optimization
Optimization methods for Machine Learning
Large Scale optimization
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
Type of Assessment
Written or oral exam on all the course subjects
Course program
Introduction; optimization models and examples
Basic definitions
Optimality conditions (unconstrained case)
Convergence of algorithms
One-dimensional optimization
Gradient descent methods
Newton methods
Conjugate direction methods
Quasi-Newton methods
Trust Region methods
Optimality conditions for constrained optimization (KKT conditions)
Constrained optimization methods
Introduction to machine learning
Stochastic gradient methods
Large scale optimization