Steepest Descent Method with Matrices

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Homework Statement

Perform the steepest descent method with exact line search for the function f(x)=(1/2)(x^T)Qx+(q^T)x-B.

Relevant Equations

f(x)=(1/2)(x^T)Qx+(q^T)x-B

We are given f(x)=(1/2)(x^T)Qx+q^Tx-B where x^k+1=x^k+α^ks^k, the search direction is s^k=-∇f(x^k). Q is a 2x2 matrix and q is 2x1 matrix and B=6. My issue is I'm confused what -∇f(x^k) is, is ∇f(x^k)=Q(x^k)-q? Just like how it is in Conjugate Gradient/Fletcher Reeve's method? Or is it Q(x^k)+q?

Thank you

 

[pasmith]

$\nabla f = \frac12(Q^T + Q)x + q$, which is $Qx + q$ if $Q$ is symmetric.