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1.3 Optimality Conditions     continued...

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.