More useful definitions, i.e., more easily identified
optimality conditions, can be provided if is a smooth function with
continuous first and second derivatives for all feasible . Then a
point is a * stationary point* of if

where is the * gradient* of . This first
derivative vector has components given by

The point is also a * strong local minimum* of
if the * Hessian* matrix ,
the symmetric matrix of second derivatives with components

is * positive-definite* at , i.e., if

This condition is a generalization of convexity, or positive curvature, to higher dimensions.