What is convex optimization?

What is convex optimization?

Convex optimization is a subfield of optimization that deals with problems where the objective function is convex, meaning any line segment between two points on the graph of the function lies above the graph itself.

Why is convex optimization important?

It's important because many real-world problems can be modeled as convex optimization problems, and they have efficient algorithms for finding global optima.

Can you give me an example of a convex optimization problem?

Sure! A common example is minimizing a quadratic function, like f(x) = x², which is convex and has a global minimum at x=0.

What are some applications of convex optimization?

Applications include machine learning, finance, engineering design, and resource allocation, among others.