Section outline

  • Teaching Unit: Methodology

    Course Title: Unconstrained Optimization

    Credits: 5

    Coefficient: 2

    Course Objectives

    This module provides an introduction to unconstrained optimization. Students who complete this course will be able to identify the fundamental tools and results in optimization, as well as the main methods used in practice. Practical sessions are included, with implementations carried out using the scientific computing software MATLAB, in order to better assimilate the theoretical concepts of the algorithms studied in the course.

    Recommended Prerequisites

    Basic knowledge of differential calculus in Rn

    Course Content

    Chapter 1: Review of Differential Calculus and Convexity

    • Differentiability, gradient, Hessian matrix

    • Taylor expansion

    • Convex functions

    Chapter 2: Unconstrained Minimization

    • Existence and uniqueness results

    • First-order optimality conditions

    • Second-order optimality conditions

    Chapter 3: Algorithms

    • Gradient method

    • Conjugate gradient method

    • Newton’s method

    • Relaxation method

    • Practical sessions

    Assessment Method

    • Final exam: 60%

    • Continuous assessment: 40%