6.12 As a result of a factorial search for the minimum of f(x1,x), the point x,x...

Transcribed Image Text:

6.12 As a result of a factorial search for the minimum of f(x1,x), the point x,x is the best yet obtained (see Figure 6-P12). Values of fat surrounding points have been generated in the factorial search; six of these values (n + 1)(n + 2)/2 of these values with n = 2-are to be fitted with a quadratic function q: q=bo + bx + bx2 + x'Ax where A = A' is a 2 x 2 matrix. The minimum point associated with q is to be found. a. Find an expression for the minimum point associated with q. b. Find expressions for the bi's and the aj's as functions of f(x,x) = faa f(xxb) = fab, f(xbx) = fa fbb fbc, fb, and the corresponding points in the x, x plane. a b Figure 6-P12. 600 + 9 6.12 As a result of a factorial search for the minimum of f(x1,x), the point x,x is the best yet obtained (see Figure 6-P12). Values of fat surrounding points have been generated in the factorial search; six of these values (n + 1)(n + 2)/2 of these values with n = 2-are to be fitted with a quadratic function q: q=bo + bx + bx2 + x'Ax where A = A' is a 2 x 2 matrix. The minimum point associated with q is to be found. a. Find an expression for the minimum point associated with q. b. Find expressions for the bi's and the aj's as functions of f(x,x) = faa f(xxb) = fab, f(xbx) = fa fbb fbc, fb, and the corresponding points in the x, x plane. a b Figure 6-P12. 600 + 9