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Introduction to Optimization in Python

Learn to solve real-world optimization problems using Python's SciPy and PuLP, covering everything from basic to constrained and complex optimization.

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4 Hours13 Videos42 Exercises

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Course Description

Optimization problems are ubiquitous in engineering, sciences, and the social sciences. This course will take you from zero optimization knowledge to a hero optimizer. You will use mathematical modeling to translate real-world problems into mathematical ones and solve them in Python using the SciPy and PuLP packages.

Apply Calculus to Unconstrained Optimization Problems with SymPy

You will start by learning the definition of an optimization problem and its use cases. You will use SymPy to apply calculus to yield analytical solutions to unconstrained optimization. You will not have to calculate derivatives or solve equations; SymPy works seamlessly! Similarly, you will use SciPy to get numerical solutions.

Tackle Complex Problems Head-On

Next, you will learn to solve linear programming problems in SciPy and PuLP. To capture real-world complexity, you will see how to apply PuLP and SciPy to solve constrained convex optimization and mixed integer optimization. By the end of this course, you will have solved real-world optimization problems, including manufacturing, profit and budgeting, resource allocation, and more.

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1
Introduction to Optimization
Free
This chapter introduces optimization, its core components, and its wide applications across industries and domains. It presents a quick, exhaustive search method for solving an optimization problem. It provides a mathematical primer for the concepts required for this course.
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Introduction to mathematical optimization
50 xp
Understanding mathematical optimization
50 xp
Applying an objective function
100 xp
Exhaustive search method
100 xp
Univariate optimization
50 xp
Finding the derivative
100 xp
Find the second derivative
100 xp
Multivariate optimization
50 xp
Partial derivatives with SymPy
100 xp
Limitations of differentiation
100 xp
2
Unconstrained and Linear Constrained Optimization
This chapter covers solving unconstrained and constrained optimization problems with differential calculus and SymPy, identifying potential pitfalls. SciPy is also introduced to solve unconstrained optimization problems, in single and multiple dimensions, numerically, with a few lines of code. The chapter goes on to solve linear programming in SciPy and PuLP.
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Unconstrained optimization
50 xp
Finding the maxima
100 xp
Multivariate optimization
100 xp
Bound-constrained optimization
50 xp
Working with Bounds
100 xp
Handling hard inequalities
100 xp
Linear programming
50 xp
What is linear programming?
50 xp
PuLP for linear optimization
100 xp
Handling multiple elements
100 xp
3
Non-linear Constrained Optimization
Free
This chapter introduces convex-constrained optimization problems with different constraints and looks at mixed integer linear programming problems, essentially linear programming problems where at least one variable is an integer.
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Convex constrained-optimization
50 xp
Interpreting indifference curves
50 xp
Visualize the indifference curve
100 xp
Utility maximization
100 xp
Convex-constrained optimization with inequality constraints
50 xp
Interior or corner?
50 xp
Linear constrained biscuits
100 xp
Nonlinear constrained biscuits
100 xp
Mixed integer linear programming (MILP)
50 xp
Adjusting MILP
100 xp
Understanding integrality
50 xp
4
Robust Optimization Techniques
This chapter covers finding the global optimum when multiple good solutions exist. We will conduct sensitivity analysis and learn linearization techniques that reduce non-linear problems to easily solvable ones with SciPy or PuLP. In terms of applications, we will solve an HR allocation with training costs problem and capital budgeting with dependent projects.
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Transforming non-linear problems
50 xp
Solving the capital budgeting problem
100 xp
Allocating resources
100 xp
Global optimization in SciPy
50 xp
Find the global optimum
100 xp
Using callback
100 xp
Sensitivity analysis in PuLP
50 xp
Slack and shadow price
50 xp
Shadow prices with juice
100 xp
The diet problem revisited
100 xp
Congratulations!
50 xp

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Collaborators

Maham Khan

Constantinos Kalfarentzos

Audio Recorded By

Jasmin Ludolf

Prerequisites

Introduction to NumPy

James Chapman

Curriculum Manager, DataCamp

James is a Curriculum Manager at DataCamp, where he collaborates with experts from industry and academia to create courses on AI, data science, and analytics. He has led nine DataCamp courses on diverse topics in Python, R, AI developer tooling, and Google Sheets. He has a Master's degree in Physics and Astronomy from Durham University, where he specialized in high-redshift quasar detection. In his spare time, he enjoys restoring retro toys and electronics.

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Jasmin Ludolf

Data Science Content Developer, DataCamp

Jasmin is a Content Developer at DataCamp. After ten years as a global marketing manager in the music industry, she recently changed careers to follow her curiosity for data. Her passion is value exchange and making data science accessible to all.