Course Syllabus: MATH 271C, Spring 2010
Instruction
- Instructor: Prof. Jiawang Nie
- Office: AP&M 5864.
- Phone: (858) 534-6015.
- Email: njw "AT" math.ucsd.edu.
- Office hours: 12:30 pm - 2:00 pm, Mondays,
and 4:00 pm - 5:30 pm, Wednesdays.
Lectures
- Time: 2:00 pm - 2:50 pm, Mondays, Wednesdays, and Fridays
- Location: APM 2402
- The following are the lecture notes of the class.
-
Week #1 Lecture 01: An Introduction to 271C
(slides)
-
Week #1 Lecture 02: Review of Eigenvalues
(slides)
-
Week #1 Lecture 03: Positive Semidefinite Matrices
(slides)
-
Week #2 Lecture 04: Matrix Norms and Inner Product
(slides)
-
Week #2 Lecture 05: Semidefinite Programming
(slides)
-
Week #2 Lecture 06: Duality Theorey in SDP
(slides)
-
Week #3 Lecture 06: Duality Theorey in SDP (continued)
-
Week #3 Lecture 06: Optimality Condition
-
Week #3 Lecture 07: Log barrier functions
(slides)
-
Week #4 Lecture 08: Central Path of SDP
(slides)
-
Week #4 Lecture 09: Interior Point Methods for SDP
(slides)
-
Week #4 Lecture 10: Representation by SDP
(slides)
-
Week #5 Lecture 11: Univariate Polynomials and Hermite Form
(slides)
-
Week #5 Lecture 12: Nonnegative Univariate Polynomials
(slides)
-
Week #5 Lecture 12: Nonnegative Univariate Polynomials (continued)
-
Week #6 Lecture 13: Minimizing Univariate Polynomials
(slides)
-
Week #6 Lecture 14: Univariate Moment Theory
(slides)
-
Week #6 Lecture 15: SOS and PSD Polynomials
(slides)
-
Week #7 Lecture 15: SOS and PSD Polynomials (continued)
-
Week #7 Lecture 16: Minimizing Multivariate Polynomials
(slides)
-
Week #7 Lecture 17: Sparse Polynomial Optimization
(slides)
-
Week #8 Lecture 18: Groups, Rings, Fields and Ideals.
(slides)
-
Week #8 Lecture 19: Groebner Basis
(slides)
-
Week #8 Lecture 20: Zero dimensional ideals and Hilbert Function
(slides)
-
Week #9 Lecture 21: Infesibilit of polynomial systems
(slides)
-
Week #9 Lecture 22: Positive Polynomial
(slides)
-
Week #9 Lecture 23: Lasserre's relaxation
(slides)
-
Week #10 Lecture 24: Multivariate Moment Problem
(slides)
-
Week #10 Lecture 25: Binary Optimization and SDP
(slides)
TA Contact Info
- There is no TA for this course.
Course Description
-
This graduate level course will focus on
convex and linear conic optimization, semidefinite programming,
algebraic and computational techniques for solving nonconvex optimization
problems involving polynomial equations and inequalities.
The course will introduce some basics in semedefinite programming,
and its applications in solving polynomial systems.
We will study both the complex and real cases, developing
techniques of general applicability, and stressing convexity-based ideas, complexity results, and
efficient implementations.
Interesting applications in engineering will aslo be shown.
-
Prerequisite
- Consent by Instructor.
Textbook
- There is no required text book. Lecture notes will be avaialable for the class.
Homework Assignments
-
Homework will be assigned and collected in Class on Wednesdays in the following weeks.
- Homework #1: due on 4/16/2010
Homework Assignment #1
- Homework #2: due on 5/05/2010
Homework Assignment #2
- Homework #3: due on 5/26/2010
Homework Assignment #3
Please write your names, ID nubmers, and section numbers on your homework,
and staple together your homework pages.
Exams
-
There will be no written exams in this class.
Project
-
Every student is required to do a research project
that uses the techniques introduced in this class,
like semidefinite programming, sum of squares, Lasserre's relaxation,
polynomial systems, etc.
Everyone need write his or her own individual report.
-
A hard copy of written project report is due in the last class.
Grading
-
The final course grade will be based on homework assignments
and project report.
-
60% Homework + 40% Project report.
Academic Integrity
-
Every student is expected to conduct themselves with academic integrity.
Any kind of cheatings is not allowed in this course.
Violations of academic integrity will be treated seriously.
-
See
UCSD Policy on Integrity of Scholarship.