Numerical Optimization ( steepest descent method)

sbashrawi

1. The problem statement, all variables and given/known data

Consider the steepest descent method with exact line searches applied to the
convex quadratic function f(x) = 1/2 xT Qx − bT x, ( T stands for transpose). show that if the initial point is such that x0 − x* ( x* is the exact solution of Qx = b) is parallel to an eigenvector of Q, then the steepest descentmethod will find the solution in one step.

2. Relevant equations



3. The attempt at a solution.

I tried to find a relation between the eigenvector and the given initial point but I couldn't