Introduction to Optimization in Python

Overview

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

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.

Syllabus

Introduction to Optimization

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.

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.

Non-linear Constrained Optimization

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.

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.