Maximum principle
In mathematics, the maximum principle is a property of solutions to certain partial differential equations, of theelliptic and parabolic types. Roughly speaking, it says that the maximum of a function in a domain is to be found on the boundary of that domain. Specifically, the strong maximum principle says that if a function achieves its maximum in the interior of the domain, the function is uniformly a constant. The weak maximum principle says that the maximum of the function is to be found on the boundary, but may re-occur in the interior as well. Other, even weaker maximum principles exist which merely bound a function in terms of its maximum on the boundary.
In convex optimization, the maximum principle states that the maximum of a convex function on a compact convex setis attained on the boundary.
