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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

So far, we've seen how we can draw a function with a single variable. The graph of the function is a curve that follows a particular pattern depending on the formula that describes the function.

This possibility of drawing the function has been very useful. It helped us solve some simple problems and understand the concept of derivatives. We strongly recommend looking at the graph of a function whenever it's possible. It's always a good start.

But unfortunately, it's not always possible to draw the graph of a function. For example, if the function has two variables instead of one, then the graph will be in 3D. The graph of the function is not a line anymore, it's a region with height, width, and depth.

We can still draw 3D graphs. But what happens when functions have more than two variables? How can we draw a 4D or 5D graph? It's impossible!



Learn to generalize the derivative to solve problems with more than one variable.

Introduction

Derivatives and Gradients

First Optimization Algorithms

Population Methods

Adding Constraints

Linear Constrained Optimization

Summary and Conclusion

Appendix

Derivatives in Multiple Dimensions