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.