Optimization and numerical methods

Objectifs

Determine the optimum of a function analytically.

Demonstrate the existence of a global optimum.

Write down the Karush-Kuhn-Tucker conditions of an optimization problem.

Numerically solve an unconstrained optimization problem.

Plan

1 Optimization :

– Reminders of differential calculus and linear algebra. General information on optimization and examples.

– Unconstrained optimization: existence, necessary conditions, sufficient conditions.

– Optimization with equality or inequality constraints: bound extrema theorems, Karush-Kuhn-Tucker theorem.

2.numerical methods :

– Gradient methods.

– Newton methods for non-linear systems.

– Direct methods for linear systems.

Prérequis

This course requires all students to master differential calculus and linear algebra.