Math 171B (Spring 2023)

Problems in all areas of mathematics, applied science, engineering, economics, medicine and statistics can be posed as mathematical optimization problems. An optimization problem begins with a set of independent variables , and often includes conditions or restrictions that define acceptable values of the variables. Such restrictions are known as the constraints of the problem. The other essential component of an optimization problem is a single measure of ``goodness'', termed the objective function, which depends in some way on the variables. The solution of an optimization problem is a set of allowed values of the variables for which the objective function assumes its ``optimal'' value. In mathematical terms, this usually involves maximizing or minimizing.

For historical reasons, the subject is often also known as mathematical programming. However, it must be emphasized that mathematical programming has no direct connection with computer programming.

Math 171B is an upper-division course that is primarily concerned with the area of nonlinear optimization, which involves the minimization of a nonlinear function subject to nonlinear constraints. Topics covered in this course include the geometry of nonlinear programming, optimality conditions, the method of gradient descent, Newton's method, penalty function methods, augmented Lagrangian methods, and interior methods.

Some programming experience is recommended. Some homework assignments will require the use of Matlab.

The aim of the class is for students to

Prerequisites: Math 171A.



Class guidelines:


instructor email office hours lectures
Philip Gill pgill@ucsd.edu Monday, Wednesday 10:30a – 11:30a
AP&M' 5872 
MWF 1:00p – 1:50p
HSS 1330
teaching assistant email office hours Thursday discussion section(s)
Xiaomeng Hu x8hu@ucsd.edu Wednesday 4:30p – 5:30p HSS 3070 A04   AP&M B412  4p
Yumeng Zhu yuz064@ucsd.edu Thursday 3p – 4p, Friday 10a – 11a HSS 3070 A01, A02   AP&M B412   1p, 2p

Midterm:

Homework:

Lecture slides:
Download lecture slides from the class calendar.

Class text and Matlab guide:
The class text is available here. The login/password is your UCSD login name (lowercase) and PID (uppercase) (e.g., 'pgill', 'A12345678').
A brief introduction to basic Matlab commands is available here.

Written assignments:
gradescope

Programming assignments:
matlab.ucsd.edu

Matlab m-files:

Important Dates:

  • Mon April 3: First lecture
  • Mon April 24: Midterm 1
  • Mon May 22: Midterm 2
  • Thu June 15 (11:30a – 2:30p): Final exam
  • UCSD Enrollment Calendar

Grades:
Course grades will be computed from the best of the following two formulas

  • homework assignments (20%), two midterm examinations (20% each), and the final examination (40%), OR
  • homework assignments (20%), best midterm examination (20%), and the final examination (60%).

Letter grades will be assigned based on the following scale: A+ > 99%, A > 93%, A- > 90%, B+ > 87%, B > 83%, B- > 80%, C+ > 77%, C > 72%, C- > 70%. I reserve the right to lower the scale (that is, any change to the scale will either improve your grade or leave it unchanged).

Textbook:
There is no required textbook for this course. A copy of "Nonlinear Programming Notes" by Philip E. Gill and Margaret H. Wright will be made available to enrolled students. Please do not distribute or repost these notes.

Written assignments:
Students will turn in written homework assignments via gradescope. See gradescope's help center for directions on submitting assignments. Written assignments can be hand-written or typed (e.g., via LaTeX). Please try to write neatly and clearly indicate the start of each problem. Remember to write your name and ID number.

Programming assignments:
Some homework assignments will require the use of Matlab. Students will be required to submit extracts of their Matlab sessions as part of their written homework assignments. All enrolled students can obtain access to Matlab at matlab.ucsd.edu.

Assignment due dates:
Due dates will be indicated in the course calendar and on the assignments.

Midterm examinations:
The midterm examinations will be held in class on the designated days.

Final examination:
Final examination is scheduled for Thursday June 15th from 11:30a to 2:30p in HSS 1330. The final will cover all material presented during the quarter.

Regrade Policy:
It is the responsibility of the student to check graded assignments and examinations and to check that there are no errors or discrepancies. Students should look over their exams and assignments after the grades are published. Any errors or discrepancies should be brought to the attention of the instructor or the teaching assistant immediately. As this course is using gradescope, regrade requests should be submitted via gradescope. However, regrade requests should be submitted in a timely manner (preferably within one week from the grades being released). Requests that arrive excessively late will be handled at the discretion of the course staff.

The login and password are your UCSD login name (lowercase) and PID (uppercase) (e.g., 'pgill', 'A12345678').

You can download written assignments below. Upload your written assignments to Gradescope from Canvas.

# Monday Tuesday Wednesday Thursday Friday
1 4/3
lec 1
lec 1 (4x1) | lec 1 (2x1)
4/5
lec 2
lec 2 (4x1) | lec 2 (2x1)



4/7
lec 3
lec 3 (4x1) | lec 3 (2x1)


2 4/10
lec 4
lec 4 (4x1) | lec 4 (2x1)
4/12
lec 5
lec 5 (4x1) | lec 5 (2x1)




Discussion Sections
4/14
lec 6
lec 6 (4x1) | lec 6 (2x1)

3 4/17
lec 7
lec 7 (4x1) | lec 7 (2x1)





4/19
lec 8
lec 8 (4x1) | lec 8 (2x1)





Discussion Sections
4/21
lec 9
lec 9 (4x1) | lec 9 (2x1)
HW1 due by 11:59pm
4 4/24
No lecture
Midterm 1
4/26
lec 10
lec 10 (4x1) | lec 10 (2x1)




Discussion Sections
4/28
lec 11
lec 11 (4x1) | lec 11 (2x1)
5 5/1
lec 12
lec 12 (4x1) | lec 12 (2x1)
HW2/MW2 due by 11:59pm
5/3
lec 13
lec 13 (4x1) | lec 13 (2x1)




Discussion Sections
5/5
lec 14
lec 14 (4x1) | lec 14 (2x1)
6 5/8
lec 15
lec 15 (4x1) | lec 15 (2x1)
5/10
lec 16
lec 16 (4x1) | lec 16 (2x1)




Discussion Sections
5/12
lec 17
lec 17 (4x1) | lec 17 (2x1) HW3/MW3 due by 11:59pm
7 5/15
lec 18
lec 18 (4x1) | lec 18 (2x1)
5/17
lec 19
lec 19 (4x1) | lec 19 (2x1)





Discussion Sections
5/19
lec 20
lec 20 (4x1) | lec 20 (2x1) HW4/MW4 due by 11:59pm
8 5/22
No lecture
Midterm 2
5/24
lec 21
lec 21 (4x1) | lec 21 (2x1)




Discussion Sections
5/26
lec 22
lec 22 (4x1) | lec 22 (2x1)
9 5/29
Memorial Day observed
5/31
lec 23
lec 23 (4x1) | lec 23 (2x1)




Discussion Sections
6/2
lec 24
lec 24 (4x1) | lec 24 (2x1)
HW5/MW5 due by 11:59pm
10 6/5
lec 25
lec 25 (4x1) | lec 25 (2x1)
6/7
lec 26
lec 26 (4x1) | lec 26 (2x1)





Discussion Sections
6/9
lec 27
lec 27 (4x1) | lec 27 (2x1)
Finals 6/12
HW6/MW6 due by 11:59pm
6/15
final exam
11:30a – 2:30p