Learn to solve optimization problems in Python using essential math tools, metaheuristic methods, and constrained optimization techniques. Master efficient solutions for real-world applications.

Optimization with Python from zero to hero.png

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Optimization theory seeks the best solution, which is pivotal for machine learning, cost-cutting in manufacturing, refining logistics, and boosting finance profits.

This course provides a detailed description of different optimization problems and the techniques used to solve them. You’ll begin with the formal definition of an optimization problem and an overview of essential mathematical tools: derivatives, gradients, and Hessian. With this knowledge, you’ll implement solutions for several optimization problems. You’ll also learn approximate metaheuristic population methods like particle swarm optimization and genetic algorithms, and solve constrained optimization problems using techniques like penalty methods and constraint simplification. Finally, you’ll solve linear programs and integer programs. 

By the end of this course, you’ll become proficient in formulating different kinds of problems as optimization problems and become skilled in the Python tools that efficiently solve these problems.

Mastering Optimization with Python

We're going to learn about **good constraints**. Those are constraints that make our lives easier.

# Getting started with equality constraints

Remember the problem of finding the smaller surface of the soda cans? Here's the problem formulation:

$$
\min_{r, h} 2\pi rh + 2\pi r^2 \\
s.t.: \pi r^2h = 355
$$

That constraint was helpful. We knew how to deal with the target functions of one variable and the constraint helped us to get rid of variable $h$.

We used the constraint to make $h$ a function of $r$:

$$
h = \frac{355}{\pi r^2}
$$

Then we transformed the target function accordingly:

$$
\min_{r} 2\pi r\frac{355}{\pi r^2} + 2\pi r^2
$$

We transformed a multivariate constrained problem into a univariate unconstrained one. A pretty good deal!

Learn to solve optimization problems with equality constraints.

Introduction

Derivatives and Gradients

First Optimization Algorithms

Population Methods

Adding Constraints

Solving Sudoku and the 8-Queens Puzzle as Constraint Satisfaction

Linear Constrained Optimization

Summary and Conclusion

Appendix

Maze Solver Using the Ant Colony Optimization Algorithm

Removing Equality Constraints

Getting started with equality constraints