Described how the resulting decision procedure for the feasibility problem can also be used to find a feasible solution via self-reducibility. Week 1 Jan Reading course with an undergrad student on approximation algorithms. Polytopes, faces, dimension of polyhedra Integral polyhedra: Defined fixed-charge flow problems.
Integer Programming The course will provide a comprehensive treatment of integer optimization including theory, algorithms and applications at the introductory graduate level. Homework submisions should have each problem starting in a fresh page. The final grade will be determined as follows: Proved the above lemma about polyhedra. Started with computational complexity. See instructor’s website Office Hours: Lecture Notes 19 Integer Linear Programming:
Shortest paths, Knapsack Week 12 Apr 7: Course Outline Integer programs are optimization models that provide a great deal of flexibility and modeling power, but are are often notoriously hard to solve and are much less understood compared to linear programs in terms of solution methods.
CSCI 5654: Linear Programming
Topics Covered Jan 5: Gave submodular-function minimization as an example. As below with the addition of ASK or Annie’s Survival Kit, three extra problems with carefully written out solutions sent weekly to better prepare the students homewoek the quizzes.
Briefly sketched how the approximate optimization problem can be reduced to the non-decision version of the feasibility problem via binary search. Solutions to Assignment 2 have been posted.
As below with the removal of one midterm and the addition of two extra-credit projects. You are allowed a grace period of upto one week for 5 assignments of your choice. Minimal faces, Extreme points, Extreme rays Feb 9: There is a typo in Q1 a in assignment 4.
Described how basic boolean logical statements can be modeled with constraints involving binary variables, which can then be combined to encode complex boolean-logic statements. Proved that the knapsack-polytope is full-dimensional and identified certain homweork and facet-defining inequalities.
Yuri Faenza – Publications
Assignment 7 is due Nov 4th wednesday. Started with the proof showing that the convex hull chvqtal integer points of a rational polyhedron is a rational polyhedron.
Stated LP duality theorem. Some specific topics to be covered are: Assignment 4 is available updated Apr Proved corollaries of the above lemma showing that a polyhedron has an essentially unique irredundant description. Research with an cvhatal student on the union-closed sets conjecture.
CO/ Integer Programming
The final grade will be determined as follows: Briefly considered the formulation with odd-cycle inequalities, and its relation to the formulation with only edge-inequalities, and the one with clique inequalities. National Math Festival in Washington D. Copying directly or indirectly consulting from unauthorized sources solution manuals, on chvtaal web pages, discussion forum and so on is prohibited. Combinatorial OptimizationB. Lecture 9 slidesmatlab codes: You are allowed to collaborate on assignments unless otherwise indicatedbut instances of collaboration should be within reason.
Homeworks, Exams We will have 4 homeworks and 2 exams. Norm minimization problems L1,L2, Linftyunconstrained least squares, solving linear systems with noise slidesmatlab codes: Prior to that, I was a student at the Massachusetts Institute of Technology where I completed a bachelor of science in mathematics as well as a bachelor of science!
This class was taught through the Prison University Projectan organization whose mission is to provide excellent higher education to people at San Quentin State Prison; to support increased access to higher education for incarcerated people; and to stimulate public awareness about higher education access and criminal justice.
Polyhedron, Decomposition theorem for polyhedron, Polytopes Week 3 Feb 3: I am interested in thinking of different ways of making math more diverse. Weekly homework and quizzes every other week, one midterm, one final. This course covered double and triple integrals in different coordinate systems, as well as line and surface integrals to culminate with Stokes’ theorem and the Divergence Theorem.