convex function

A convex function is a type of mathematical function where, if you pick any two points on its graph, the line segment connecting those points lies above or on the graph itself. This means the function has a "bowl-shaped" curve, curving upward with no dips or inward curves. Convex functions are important in optimization because any local minimum is also a global minimum, making it easier to find the lowest point of the function. They often appear in areas like economics, machine learning, and data analysis where finding optimal solutions is essential.