Fenchel duality

Fenchel duality is a concept in optimization that connects two mathematical problems: a primal problem and its dual. It shows that solving the primal problem can provide insights into the dual problem, and vice versa. The relationship allows us to find solutions more efficiently or to understand the structure of the problems better. Essentially, it highlights how maximizing or minimizing one function can be related to minimizing or maximizing another, offering a broader perspective on finding optimal solutions. This dual approach is widely used in economics, optimization theory, and various fields requiring resource allocation.