Convex optimization is a subfield of mathematical optimization that focuses on the problem of minimizing convex functions over convex sets. Convex functions are mathematical functions that have certain properties that make optimization easier, such as having a unique global minimum. Convex optimization has a wide range of applications in engineering, economics, statistics, machine learning, and many other fields. It is a powerful tool for solving complex optimization problems efficiently and reliably. Some common algorithms used in convex optimization include gradient descent, Newton's method, and interior-point methods.