Math 661: Optimization --- Fall 2020
To contact the instructor: j.rhodes@alaska.edu
Course syllabus: M661syl.pdf
Homework Assignments:
The dates below are when problems were assigned. Unless otherwise noted, problems from Griva, Nash, & Sofer, and are always due the following Monday.
- 8/24: #1 Solve the fence problem from lecture by a) a Calc I approach, and b) Using Lagrange multipliers as in Calc III.
#2 Use the same two approaches to find the maximizer of f(x,y)=x^2-y^2 on the unit circle.
- 8/26: pdf
- 8/28: pdf
- 8/31: p. 12, #4.1
- 9/2: p. 47 #2.1, 2.3, 2.4
- 9/4: p. 52 #3.1, 3.2, 3.3; #1 Using the definition of convexity and algebra (no derivatives)
show that a quadratic function of 1 variable f(x)=a+bx+cx^2 with c>0 is convex on the real line.
- 9/9: p. 52 #3.10, 3.13, 3.19, 3.20
- 9/11: p. 66 #6.4, 6.5
- 9/14: p. 74 #7.1, 7.10 (You should write computer code, perhaps by modifying my MATLAB newton.m, to do these.
- 9/16: p. 61 #5.1
- 9/18: #1 Investigate the impact of repeated roots on the convergence rate of Newton's Method as follows: Consider the functions
f(x)=(x-2)(x-1), g(x)=(x-2)^2, and h(x)=(x-2)^3, with x*=2 as the desired root. Using x_0=3 as an initial guess for all,
apply Netwon's method computing the error e_i=x_i-x* for each iteration. Stop the iteration when |e_i|<10^-12. You should turn
in your list of successive errors for each function, the number of iterations needed for each function, your guess as to the
convergence rate, and your reasoning. Do not turn in computer code.
- 9/21: p. 362, # 2.2, 2.3, 2.5, 2.7, 2.10
- 9/23: p. 369, # 3.2, 3.3
- 9/25: p. 374, # 4.1 (D must have positive diagonal entries here), 4.4, 4.6
- 9/28: pdf
- 9/30: p. 385, # 5.2, 5.3, 5.4, 5.9
- 10/2: none
- 10/5: p. 408, # 2.1, 2.2 (Program this, with exact line search formula. This is not a general purpose program, and you do not need to turn in your code.)
- 10/7: p. 420, #3.1
- 10/14: p. 420, #3.8, 3.9; p.489, #2.1, 2.4, 2.7
- 10/16: none
- 10/19: p. 493, #3.1
- 10/21: p. 501, #4.1 ("Solve" means use 1st order necessary conditions, after first stating constraints as Ax>=b)
- 10/23: none
- 10/26: p. 99, #1.1(i); p. 105, #2.3
- 10/28: none
- 10/30: p. 123, #4.4
- 11/2: p. 141, #2.2 (iii) and (vi)
- 11/4: p. 148, #3.1 (i)
- 11/6: none
- 11/9: p. 159, #4.1, 4.2(a)
- 11/11: none
- 11/13: p.177, #1.1, 1.3
- 11/16: p.185, #2.1, 2.15
- 11/18: none
- 11/20: none
- 11/23: none
- 11/30: p. 194, #3.1, 3.2
- 12/2: none
- 12/4: none
Final Exam: Monday, Dec. 7, 11:15-2:15; Chapman 104