Gain insights into solving optimization problems in Python. Delve into essential mathematical tools, metaheuristic methods, and techniques for constrained optimization. Become proficient in efficient Python solutions.

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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

We already know how to define an integer problem mathematically. In this lesson, we'll solve an integer problem using ```cvxpy```. Let's find out what the problem is about.

## The knapsack problem

The salesman is moving from one city to another. Unfortunately, he can't carry all his possessions. He has a knapsack that can carry up to $w$ kilograms, so he can't load more than that weight. The salesman has a list of all the items he has with the weight and value of each item. He has to try to decide what items to carry with him, so he gets the maximum possible value without exceeding the weight that the knapsack can load.

We already know how to define an integer problem mathematically. In this lesson, we'll solve an integer problem using ```cvxpy```. Let's find out what the problem is about.

# The knapsack problem

The salesman is moving from one city to another. Unfortunately, he can't carry all his possessions. He has a knapsack that can carry up to $w$ kilograms, so he can't load more than that weight. The salesman has a list of all the items he has with the weight and value of each item. He has to try to decide what items to carry with him, so he gets the maximum possible value without exceeding the weight that the knapsack can load.

Learn to solve the famous knapsack problem using integer programming with CVXPY.

Introduction

Derivatives and Gradients

First Optimization Algorithms

Population Methods

Adding Constraints

Linear Constrained Optimization

Summary and Conclusion

Appendix

Solving Integer Problems with CVXPY

The knapsack problem