Optimization: principles and algorithms - Unconstrained nonlinear optimization

Introduction to unconstrained nonlinear optimization, Newton’s algorithms and descent methods.

The course is structured into 6 sections:

• Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem.
• Objective function: you will review the mathematical properties of the objective function that are important in optimization.
• Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution.
• Solving equations, Newton: this is a reminder about Newton's method to solve nonlinear equations.
• Newton's local method: you will see how to interpret and adapt Newton's method in the context of optimization.
• Descent methods: you will learn the family of descent methods, and its connection with Newton's method.