MATH 5770-01, MATH 6640-01, ME EN 6025-01 — Introduction to Optimization
Fall 2021
| Instructor: |
Akil Narayan |
| Email: |
akil sci.utah.edu |
| Office phone: |
+1 801-581-8984 |
| Office location: |
WEB 4666, LCB 116 |
| Office hours: |
Tuesday, 11am-12pm, Friday 3pm-4pm, WEB 4666 and virtual (Zoom) |
| Class meeting time: |
Tuesday, Thursday 9:10am - 10:30am |
| Class meeting location: |
WEB L114 |
| Textbook (required): |
Amir Beck. Introduction to Nonlinear Optimization, ISBN-13 978-1-61197-364-8 |
Existence, uniqueness and characterization of solutions to finite dimensional unconstrained and constrained optimization problems. Solution methods for finite dimensional unconstrained and constrained optimization problems. Newton and Quasi-Newton methods. Globalization strategies. Linear Programming. Least Squares. Quadratic Programming. Convex Programming.
The course syllabus is here: PDF
Graded assignments
Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.
Homework assignments
Homework will be collected in-class on Tuesdays.
Late work will not be accepted without advance approval from the instructor.
|
Problem set description
|
Due date
|
Homework
|
|
1 : Euclidean space
|
September 7, 2021
|
PDF
|
|
: Solutions
|
|
PDF
|
|
2 : Optimality conditions
|
September 21, 2021
|
PDF
|
|
: Solutions
|
|
PDF
|
|
3 : Least squares and gradient descent
|
October 5, 2021
|
PDF
|
|
: Solutions
|
|
PDF
|
|
4 : Newton's method and convex sets
|
November 2, 2021
|
PDF
|
|
: Solutions
|
|
PDF
|
|
5 : Convex functions
|
November 16, 2021
|
PDF
|
|
: Solutions
|
|
PDF
|
|
6 : Convex optimization
|
December 7, 2021
|
PDF
|
|
: Solutions
|
|
PDF
|
Miscellaneous handouts
The following are various relevant handouts.
|
Description
|
Posting date
|
Download
|
|
Lecture 01 slides: Preliminaries
|
August 26, 2021
|
PDF
|
|
Lecture 02 slides: Eigenvalues and eigenvectors
|
August 31, 2021
|
PDF
|
|
Lecture 03 slides: Basic topology
|
September 2, 2021
|
PDF
|
|
Lecture 04 slides: Optima and first-order optimality
|
September 7, 2021
|
PDF
|
|
Lecture 05 slides: Definite matrices
|
September 14, 2021
|
PDF
|
|
Lecture 06 slides: Second-order optimality
|
September 21, 2021
|
PDF
|
|
Lecture 07 slides: Least squares problems
|
September 21, 2021
|
PDF
|
|
Lecture 08 slides: Regularization and least squares
|
September 23, 2021
|
PDF
|
|
Lecture 09 slides: Descent methods
|
October 2, 2021
|
PDF
|
|
Midterm jeview session
|
October 6, 2021
|
PDF
|
|
Lecture 10 slides: Newton's method
|
October 21, 2021
|
PDF
|
|
Lecture 11 slides: Cholesky factorizations
|
October 21, 2021
|
PDF
|
|
Lecture 12 slides: Convex sets
|
October 26, 2021
|
PDF
|
|
Lecture 13 slides: Convex functions
|
November 4, 2021
|
PDF
|
|
Lecture 14 slides: Convex functions II
|
November 9, 2021
|
PDF
|
|
Lecture 15 slides: Convex optimization
|
November 18, 2021
|
PDF
|
|
Lecture 16 slides: The KKT conditions
|
December 7, 2021
|
PDF
|
Software
The following are links to software used during class demonstrations.
|
Description
|
Language
|
Download
|
|
In-class code demos
|
Python
|
github
|
Resources
Book website
Linear algebra review
Multivariable calculus review
|