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Suppose p is a descent direction and define o(a) = f (3 + ap), a>0. Then any minimizer a* of o(a) satisfies o'(a*) = f(x+a*p)?p=0. A strongly convex quadratic function has the form Oc+672. Q>0, and hence Vf(1) = Qx +b. The one-dimensional minimizer is unique, and by Equation (2) satisfies (3) (Q(2+a*p) +b?p=0. Therefore (Qr+b)+p+a*pQp=0 which together with Equation (3) gives a* = _(Qr+b)p Vf(r)"p PT Qp pTQp Suppose p is a descent direction and define o(a) = f (3 + ap), a>0. Then any minimizer a* of o(a) satisfies o'(a*) = f(x+a*p)?p=0. A strongly convex quadratic function has the form Oc+672. Q>0, and hence Vf(1) = Qx +b. The one-dimensional minimizer is unique, and by Equation (2) satisfies (3) (Q(2+a*p) +b?p=0. Therefore (Qr+b)+p+a*pQp=0 which together with Equation (3) gives a* = _(Qr+b)p Vf(r)"p PT Qp pTQp