Non-Linear Programming

This chapter provides an introduction to Non-Linear Programming (NLP), the branch of optimisation that deals with problem models where the functions that define the relationship between the unknowns (either objective function or constraints) are not linear. The fact that the functions are not linear makes NLP a lot harder to deal with from a mathematical point of view. The chapter will focus on specific cases that have many applications in real life problems, particularly quadratic functions and their relationship to machine learning.

Tutorials

This section contains some basic tutorials:

Contents:

• Introduction to Non-Linear Programming
• Unconstrained NLP
• Gradient descent methods
• Interactive Gradient-Descent in Python
• Questions
• Constrained NLP
• Introduction to machine learning
• Quadratic Optimization and Machine Learning
• Support Vector Machines

Exercises

In this section you have a collection of CLP problems sorted by difficulty:

• Easy problems: You can tackle these problems after the first lesson on NLP.

• Normal problems: These problems require that you are familiar with concepts like Kuhn Tucker conditions.

• Hard problems: This is the type of problems that definitively get you ready for the exam.

Contents:

• Planning the construction of homes (easy)
• Car Production Planning (normal)
• Nova Case (normal)
• Maximising investments of a startup (hard)
• Planning refreshments production (hard)
• Production Mix of Pharma (normal)
• Optimising the design of headphones (normal)
• Mathematical Nirvana (normal)

Solved Exercises

In this section you have the solution to the different exercises.

Contents:

• Planning the construction of homes (easy)
• Car Production Planning (normal)
• Nova Case (normal)
• Maximising investments of a startup (hard)
• Planning refreshments production (hard)
• Production Mix of Pharma (normal)
• Optimising the design of headphones (normal)
• Mathematical Nirvana (normal)