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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

In this lesson, we're going to learn how to use derivatives to solve optimization problems. The derivative of a function tells us a lot of information about that function, including what points could be the local minima or maxima.

## Local minima and maxima

Consider the following function:

In this lesson, we're going to learn how to use derivatives to solve optimization problems. The derivative of a function tells us a lot of information about that function, including what points could be the local minima or maxima.

# Local minima and maxima

Consider the following function:

Learn about derivatives and their importance in optimization problems.

Introduction

Derivatives and Gradients

First Optimization Algorithms

Population Methods

Adding Constraints

Linear Constrained Optimization

Summary and Conclusion

Appendix

Derivatives

Local minima and maxima