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Welcome to 6.256/18.456 Semidefinite Optimization!
The first lecture of this course is Wednesday 2/17 at 1pm EST on Zoom.
Please see the syllabus for full details.
Lecture Notes
- Wed Feb 17: Lecture 1: What is this course about? Download Lecture 1: What is this course about? - Slides Download Slides
- Fri Feb 19: Lecture 2: Semidefinite programming. Download Lecture 2: Semidefinite programming. - Slides Download Slides
- Wed Feb 24: Lecture 3: Binary quadratic optimization Download Lecture 3: Binary quadratic optimization
- Wed Mar 3: Lecture 4: Algebra Review Download Lecture 4: Algebra Review
- Wed Mar 10: Lecture 5: Univariate Polynomials Download Lecture 5: Univariate Polynomials
- Fri Mar 12: Lecture 6: Resultants and Discriminants Download Lecture 6: Resultants and Discriminants
- Fri Mar 19: Lecture 7: Binomial equations and Newton polytopes Download Lecture 7: Binomial equations and Newton polytopes
- Wed Mar 24: Lecture 8: Sum of Squares Download Lecture 8: Sum of Squares
- Wed Mar 31: Lecture 9: SOS Applications Download Lecture 9: SOS Applications
- Fri Apr 2: Lecture 10: Duality and Moments Download Lecture 10: Duality and Moments
- Wed Apr 7: Lecture 11: Ideals and Varieties Download Lecture 11: Ideals and Varieties
- Fri Apr 9: Lecture 12: Monomial Orderings and Groebner Bases Download Lecture 12: Monomial Orderings and Groebner Bases
- Wed Apr 14: Lecture 13: Zero dimensional systems Download Lecture 13: Zero dimensional systems
- Wed Apr 21: Lecture 14: SOS on quotients
Download Lecture 14: SOS on quotients
Lecture 15: Infeasibility Download Lecture 15: Infeasibility and Certificates Download Certificates - Fri Apr 23: Lecture 16: Quantifier Elimination Download Lecture 16: Quantifier Elimination
- Wed Apr 28: Lecture 17: Psatz revisited / Copositivity Download Lecture 17: Psatz revisited / Copositivity
- Fri Apr 30: Lecture 18: Representations of positive polynomials Download Lecture 18: Representations of positive polynomials
- Wed May 5: Lecture 19: Symmetry reduction Download Lecture 19: Symmetry reduction
Forum/Discussions:
We will be using Ed (edstem.org Links to an external site.) for class discussions.
The course website is edstem.org/us/courses/3073 Links to an external site.
Grading
Grading is split evenly (50/50) between:
1. Problem sets (total ~7, approximately one pset every two weeks)
2. Class project.
There is no final exam.
Links
Pset Partners: This is a new MIT problem-set partner-matching website. Please check it out, and sign up!
Getting started with Sum Of Squares: