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cvxpy

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

Until now, we've had a broad theoretical background in optimization. We've understood some algorithms and the importance of derivatives, gradients, and Hessians. To better grasp all this knowledge, we've implemented all the algorithms we've seen so far. Implementing our version of the algorithms is a great exercise that allows us to develop a deeper understanding of all the different elements that are involved when solving a problem.

As we've seen when visiting gradient descent or Newton's method, there are advanced versions of these algorithms out there that can deal with saddle points and convergence in a better way. Explaining the details of those advanced algorithms is beyond the scope of this course, but that doesn't mean we can't use them. Once again, a Python library will allow us to do it: SciPy.

Our versions have been implemented in problems with just one variable. But real-life problems, like training machine learning models, can involve hundreds or thousands of variables. The versions provided by SciPy will handle multiple variables for us. Nevertheless, to effectively use SciPy, we need to know about the best ways to operate with so many variables. So let's dive into SciPy and its advanced algorithms.



Learn to apply gradient descent and Newton's method to problems with several variables.

Introduction

Derivatives and Gradients

First Optimization Algorithms

Population Methods

Adding Constraints

Linear Constrained Optimization

Summary and Conclusion

Appendix

Multiple Variables Using SciPy