Convex Analysis

Convex analysis is a branch of mathematics that studies convex sets and convex functions. A set is convex if, for any two points within it, the straight line connecting them also lies entirely inside the set. Convex functions, on the other hand, exhibit a “bowl” shape, meaning that a line segment between any two points on the graph lies above or on the graph itself. This field is crucial in optimization, economics, and decision-making, as it simplifies many problems by ensuring that local solutions are also global solutions, making it easier to find the best outcomes.