To contact the instructor: j.rhodes@alaska.edu

Course syllabus: M661syl.pdf

Matlab m-files (and errata) for Ferris, Mangasarian, & Wright are available here: http://www.cs.wisc.edu/math-prog/lpbook/

The dates below are when problems were assigned. Unless otherwise noted, problems are always due the following Monday.

Problems are from Nocedal & Wright, unless otherwise stated.

- 9/6 none
- 9/9 Read Chapter 1; (1) Show, using the definition of convex, that a region defined by linear equalities and inequalities written in matrix form as Ax=b, Cx \le d is convex. ('\le' means 'less than or equal to') (2) Show, using the definition of convex, that (a) f(x)=x^2 is strictly convex on R, (b) f(x)=x is convex on R, and (c) f(x,y)=x^2+y^2 is strictly convex on R^2.
- 9/11 Begin reading Chapter 2; (3) Show, using the definition of convex, that f(x,y)=x^2-y^2 is neither convex nor concave on R^2. (4) For f(x,y)=x^2+y^2, specify two different domains (subsets of R^2) which are not convex, such that f has a unique minimum on the first, but not on the second.
- 9/13 (5) Suppose f: S --> R is convex. Show that any local minimizer of f is a global minimizer. (Hint: Suppose x_1 is a local minimizer, and f(x_2) < f(x_1), and find a contradiction.)
- 9/16 2.1,2,3,7,8
- 9/18 none
- 9/20 none
- 9/23 none
- 9/23 (extra meeting) 2.9,13,14,15
- 9/25 3.1 (due on 10/2)
- 9/27 none
- 9/30 none
- 9/30 (extra meeting) 3.2,3,6; Compute the condition number of the Hessian of the Rosenbrock function at its minimizer.
- 10/2 none
- 10/4 5.2,3
- 10/7 (1) Let A be symmetric positive definite. Give formulas for a generalization of the Gram-Schmidt process that take vectors v_1, v_2,v_3, and produces vectors w_1,w_2,w_3 that are A-conjugate, with A-length 1. Show your formulas are correct by showing each of the 3 possible pairs of w_i vectors is A-conjugate, and that each w_i does have the correct A-length. (2) Demonstrate your GS-like process for the matrix A=[1 1 0; 1 2 1; 0 1 2] and vectors v_1=(1,0,0), v_2=(0,1,0),v_3=(0,0,1).
- 10/7 (extra meeting) none
- 10/9 5.5, 6, 1(use MATLAB command 'hilb')
- 10/11none
- 10/14 (NO extra meeting)
- 10/16 none
- 10/18 none
- 10/21-25 Take-home exam, no classes
- 10/28 none
- 10/30 12.20,21,18,15,14
- 11/1 none

- 11/4 none
- 11/6 Handout with 3 problems, 1-1-1
- 11/8 none
- 11/11none
- 11/11 (extra class) 2-2-3, 2-3-3, 2-3-4, 2-4-2, 2-4-3, 2-4-6, 2-4-7
- 11/13 3-1-2, 3-3-2, 3-3-4, 3-3-5, 3-3-6, 3-3-7
- 11/15 none
- 11/18 3-4-2, -3, -4, 3-5-3, -4
- 11/20 3-6-2, -6, -7, -9, -10, -12, -14, -15
- 11/22 none
- 11/25 4-2-2, 4-4-1, -2, -3
- 11/27 none
- 11/29 THANKSGIVING BREAK
- 12/2 4-5-2
- 12/4 4-6-2, -4, 4-7-1, -4, -5, -6
- 12/6 4-9-1, -3
- 12/9 none
- 12/11 Final Exam handed out
- 12/13 none