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Principles of Optimization
Math 364

Important Information

Here is the course Syllabus.


Here is the course textbook (updated August 15).

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.

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) [Th Oct 24] Chapter 11, Exercise 8

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.

Final Exam

Date: Thursday, December 12
Time: 10:10AM -- 12:10PM
Place: TBD (likely our normal classroom)

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.


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.

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


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