In the constrained optimization problem

suppose that f is concave and G(θ) convex. Then every local optimum is a global optimum.
Another distinction we need to note is that between strict and non strict optima. A point x* A ˆˆ y is a strict local optimum if it is strictly better than all feasible points in a neighborhood S, that is,

It is a strict global optimum if it is ``simply the best,'' that is,

max f(x,0) xeG(O) f(x ,0) > f(x, for every x E SnG(0) f(x ,0)> f(x, ) for every x e G(0)