Contact About 564 364 Research Publications Extras

My Contact Info

Find Me:

  • Office: Neill 228
  • email:

Office Hours:

  • MonWed 11:00 - 12:00
  • TueThu 9:00 - 10:00
  • and by appointment


  • Department of Mathematics
  • 103 Neill Hall
  • P.O. Box 643113
  • Washington State University
  • Pullman, WA 99164-3113

Principles of Optimization
Math 364

Important Information

Here is the course Syllabus.


Here is the course textbook (updated November 6).
Here is Chapter 16.

Here is the software you will need to complete much of the homework:

Homework Self-Study

Be able to complete all of the Exercises presented in the text. This should be the focus of your self-study. For problems to be turned in and graded, see the next section.

Here are a few examples of well-written homework problem solutions. Updated Friday September 27.

Here are some Quiz Solutions. Updated Sunday September 29.

In this paper, you can read how Dantzig describes the circumstanced behind the development and implementation of the Simplex Method.

Here is a compilation of the quizzes.

Homework for Submission

(##) [Due Date] Assignment
(01) [Th Aug 22] Chapter 2, Exercise 1
(02) [Tu Aug 27] Chapter 2, Exercise 8
(03) [Th Aug 29] Chapter 3, Exercise 4
(04) [Tu Sep 03] Chapter 3, Exercises 5c and 8c
(05) [Th Sep 05] Chapter 4, Exercise 4
(06) [Tu Sep 10] Chapter 4, Exercises 6a and 6b
(07) [Th Sep 12] Chapter 5, Exercise 2
(08) [Tu Sep 17] Chapter 6, Exercise 2
(09) [Th Sep 19] Chapter 7, Exercise 1a
(10) [Tu Sep 24] Chapter 7, Exercise 2
(11) [Th Sep 26] Chapter 8, Exercise 7a and 7b
(12) [Tu Oct 01] Chapter 9, Exercise 5
(13) [Th Oct 03] Chapter 11, Exercise 1 (not modeling problem 1)
(14) [Tu Oct 08] Chapter 11, Exercise 2 (not modeling problem 2)
(15) [Th Oct 10] Chapter 11, Exercise 3 (not modeling problem 3)
(16) [Tu Oct 15] Chapter 11, Exercise 4
(17) [Th Oct 17] Chapter 11, Modeling Problem 9 (start early)
(18) [Tu Oct 22] Chapter 11, Modeling Problem 5
(19) [Tu Oct 29] Chapter 11, Exercise 8
(20) [Th Oct 31] Chapter 11, Modeling Problem 4
(21) [Tu Nov 05] Chapter 11, Modeling Problem 13
(22) [Th Nov 07] Chapter 11, Modeling Problem 18
(23) [Tu Nov 12] Chapter 11, Exercise 17
(24) [Th Nov 14] Chapter 12, Exercise 3
(25) [Tu Nov 19] Chapter 13, Exercise 7(a,b)
(26) [Th Nov 21] Chapter 13, Exercise 7(c,d)
(27) [Tu Dec 03] Chapter 13, Exercise 7e
(28) [Th Dec 05] Chapter 16, Exercise 1b

Midterm Exam

Date: Thursday, October 3
Time: during normal class time
Place: we will use our normal classroom
Please read the cover sheet of the exam before coming to the exam.

Check out the solutions.

Final Exam

Date: Thursday, December 12
Time: 10:10AM -- 12:10PM
Place: We will use our normal classroom.
I am providing a few practice exams. Please note that the content will have significant overlap with the topics we studied in class. However, they may also include topics which we did not consider. Practice Exams: Exam1, Exam2, Exam3.

Here are selected solutions to the practice exams. Beware! My solutions have not been carefully checked and there are problems with the questions on Exam2 -- but the flavor of the questions is still good.

The exam will have one question asking you to compose an executive summary. The problem of interest is Modeling Problem 19 (page 146 of the text). The solution will be provided on the exam, but you may wish to solve the problem and think about the solution before the exam.

Convex and Nonlinear Optimization
Math 564


Course Syllabus

A proof that Compass Search convergest to a stationary point.

Notes on Optimization Over a Simplex.

Notes on Feasible Direction Methods.

Papers on Total Variation Denoising: RyOsFa1992.pdf, Ch2004.pdf, ChGoMu1999.pdf, GoYi2005.pdf.


As part of your homework, you will need to formally define various mathematical terms. What follows is a list of terms that you should include, though it may not be complete. This list will be regularly updated.

unconstrained local minimum (maximum)
unconstrainted global minimum (maximum)
stationary point
singular, nonsingular
locally stable
isolated stationary point

Homework Assignments

Your homework will be collected in a single document which you will keep at and you must provide me with edit priviledges (for feedback and grading). You may wish to start with this homework assignment template and example figure.

Section 1.1, Exercises 1,2,4,8.
Section 1.2, Exercises 1,3,7,12.
Section 1.3, Exercises 1,3.
Section 1.4, Exercises 1,8.
Section 1.6, Exercise: On page 145 of the text, Bertsekas states "These estimates suggest a more favorable convergence rate than the one of steepest descent." Justify this statement.
Section 1.7, Quasi-Newton Homework.
Section 1.8, Show that for a strictly convex function, the Nelder-Mead Simplex method never utilizes the shrink step.
Section 2.1, Exercises 8,11(part 3)
Section 2.2, Optimization over a Simplex Homework.
Section 2.3, Gradient Projection Homework.
Section 3.1, Equality Constrained Optimization Homework.
Section 3.3, Exercise 3.
Section 4.2, Exercises 1,2. Data for part (b) of Exercise 2

Midterm Exam #1

Date: Monday, September 16
Time: 9:10AM - 10:00AM
Place: CUE 409
Here is the takehome question.

Midterm Exam #2

Date: Monday, October 14
Time: 9:10AM - 10:00AM
Place: CUE 409

Midterm Exam #3

Date: Wednesday, November 13
Time: 9:10AM - 10:00AM
Place: CUE 409

Final Exam

Date: Friday, December 13
Time: 8:00AM - 10:00AM
Place: CUE 409


Coming Soon!



I like to write short human interest pieces.

I like to ask questions.

Classic video game buff? Check out the entertaining documentary that includes me! Man vs Snake