# CHVATAL RANK HOMEWORK

Due on April 3, This course covered some introductory topics in combinatorics, probability, statistics, linear algebra and optimization. The final exam will be a take-home exam. Assignment 6 is due on the 28th of october. Linear Programming by R. Theory and Applications by G.

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. Defined the notion of a polytime reduction. Homeworks will be posted in Compass2g. This class was taught through the Prison University Project , an 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. Started with polyhedral theory. Some subset of the following topics will be covered.

Analysis of Network Simplex Problems.

Described and analyzed the Ellipsoid method assuming the underlying set K is closed, convex, contained in a bounding ball, and contains a ball.

No partial credit for partial correctness.

## CO452/652: Integer Programming

This course covered various topics connected to matchings and matroids from a polyhedral perspective. Posted lecture 3 slides and Handout 2. Due on Thu, Mar 9 Exam 1.

Described the generic branch-and-bound BnB approach. Solutions to Assignment 3 have been posted. I am interested in thinking of different ways of making math more diverse.

Definition of a cone. Proved the equivalence of finitely generated cones and polyhedral cones. Optimality, Relaxations, Bounds Week 2 Jan Defined separation oracle, ellipsoid, affine transformation, and the notion of volume.

Described applications of the Ellipsoid method to combinatorial optimization, where it is often “easy” to obtain a separation oracle, and ensure that the assumptions of boundedness and enclosing-ball hold, by adhoc means if necessary. Finished the above proof.

# CO/ Integer Programming

Due on Thu, Feb 19 Homework 2. National Math Festival in Washington D.

Reading course with an undergrad student on approximation algorithms. Electronic submission will be accepted provided it is in a “single file pdf” format. Weekly homework and quizzes every cvhatal week, one midterm, one final. Hee Youn Kwon Office hours: Assignment 3 here is due on the 28th Sept. If in doubt, ask the instructor. Dynamic Programming technique contdApplns: Polytopes, faces, dimension of polyhedra Integral chvafal Total Dual Integrality, Appln: Stated that the cutting plane method with Gomory cuts has finite convergence.

CURRICULUM VITAE LAUREATO CTF

# Yuri Faenza – Publications

Mentioned how the Ellipsoid method can be modified for linear optimization. Mentioned the issue of precision that arises in the Ellipsoid method. You are allowed to collaborate on assignments unless otherwise indicatedbut instances of collaboration should be within reason. Spring Break Week 11 Mar Showed that the formulation with clique inequalities is stronger, and argued that the clique-inequalities are facet-defining.

Due on Tue, Apr 25 Exam 2. Started with computational complexity. Showed how the above can be applied to the BCC lift-and-project operator.