Computer Science 6676, Spring 1999                                         April 7, 1999

Assignment 6

Due Wednesday, April 21

  1. Chapter 8, problem 3a.
  1. Show that the update formula
    1. A_+  =   A_c   +   [(y - A_c   s)   v^T ]   /   (v^T s)

    satisfies the secant equation   A s = y   for any vector v for which   v^T s   is not zero.

  1. Chapter 9, problem 9.
  1. Chapter 9, problem 20.


Class Project, Phase III

Due Wednesday, April 21

  1. Enlarge your driver program for unconstrained optimization so that it also has the option of running a BFGS secant method, using the unfactored version. This will require coding the new routines INITHESSUNFAC and BFGSUNFAC and replacing the calls to the finite difference Hessian in the initialization and iteration sections of the driver with calls to these two routines, as shown in Algorithm D6.1.1 (the main driver for unconstrained optimization). Once again, you do not need to implement scaling (equivalently, you may assume typx(i) = S_x (i) = 1 for each i, and typf = 1).
  1. Verify that your program runs correctly on the same problems as for Phase II of the project, from the same starting points. Use the same stopping tolerances as in Phase II. Once again, for each problem, print the termination code, final value of x, function value at that point, and the number of iterations taken. Also tabulate and print the total number of function evaluations taken, including those used for finite difference derivatives. Also do this for Newton's method for each of the same problems, and for each problem, compare the cost in iterations, and in total function evaluations, for the BFGS and Newton's methods.