Advanced · Research
Convex optimization
Visual diagram · (in preparation) · Math · (in preparation) · Worked example · 3 difficulty levels.
TL;DR. Finding the minimum value of a convex function using mathematical methods like gradient descent, ensuring a global minimum is found.
Technical Definition
Finding the minimum value of a convex function using mathematical methods like gradient descent, ensuring a global minimum is found.
How it works
Convex optimization is a field of mathematics focused on finding the minimum (or maximum) of convex functions. Techniques like gradient descent are commonly employed. A significant advantage of convex optimization problems is that any local minimum found is guaranteed to also be the global minimum. Much machine learning research is dedicated to formulating problems as convex optimization tasks and developing efficient algorithms to solve them.
Related Concepts
- Gradient Descent — An optimization algorithm that iteratively adjusts model parameters by moving in the direction of steepest decrease of the loss function.
- Optimization — The mathematical process of finding parameter values that minimize a loss function.
- Convex function — A mathematical function shaped like a 'U', where the line segment connecting any two points on the graph lies above or on the graph itself.