www-ai.cs.tu-dortmund.de/LEHRE/VORLESUNGEN/NOPT/SS14/hw/hw-04.pdf
sTk yk > 0.
3.[5] Show that n nonzero conjugate vectors {p0, p1, . . . , pn−1}, pi ∈ Rn, with respect to a symmetric positive definite matrix A are linearly independent, i.e., if
∑n−1 i=0 cipi = 0
for any [...] the curvature condition sTk yk > 0, with sk = xk+1 − xk and yk = ∇f(xk+1)−∇f(xk), holds for any xk+1 and xk in Rn.
2.[5] Show that the second strong Wolfe condition (with 0 < c2 < 1) with a descent direction [...] any c = (c0, c1, . . . , cn−1) T , then c must be a zero vector.
4.[10] Implement the conjugate gradient algorithm (Algorithm 2 in Lecture 13), and use it to find Newton directions instead of using matrix …
