Quadratic Functions

Preliminaries Linear algebra Calculus 1,2 Taylor series Quadratic Functions1 Quadratic function, a type of performance index, is universal. One of its key properties is that it can be represented in a second-order Taylor series precisely.
[ F(mathbf{x})=frac{1}{2}mathbf{x}^TAmathbf{x}+mathbf{d}mathbf{x}+ctag{1} ]
where (A) is a symmetric matrix(if it is not symmetric, it can be easily converted into symmetric). And recall the property of gradient:
[ nabla (mathbf{h}^Tmathbf{x})=nabla (mathbf{x}^Tmathbf{h})=mathbf{h}tag{2} ]
and
[ nabla (mathbf{x}^TQmathbf{x})=Qmathbf{x}+Q^Tmathbf{x}=2Qmathbf{x}tag{3} ]