# CHVATAL RANK HOMEWORK

Homework Assignment 4 here is due on monday 5th October one week late: Valid inequalities and procedures for generating them. Bipartite Matchings Mar Characterization of extreme points, Representation of polyhedron Feb Proved lemma relating the dimension of a polyhedron P to the rank of the subsystem consisting of its implicit equalities, and characterized the facets of P as its faces of dimension dim P Assignment problem, matchings in bipartite graphs, Network flows Week 6 Feb

Homeworks, Exams Midterm and Final will be in-class written exams. Shortest paths, Knapsack Week 12 Apr 7: Showed how the full-dimensionality assumption can be dropped for an explicitly-described polyhedron K by perturbing the RHS of the constraints. Mathematical maturity at the level of a beginning graduate student will be assumed. Gave an overview of the simplex method.

Topics not covered in Chvatal will be covered by notes and handouts. Showed how these inequalities can be used to obtain valid inequalities for the homeworrk facility location problem by aggregating clients and facilities. Topics Covered Jan 5: The following books may be used as reference books.

As below with the removal of one midterm and the addition of two extra-credit projects.

## CO452/652: Integer Programming

Proved Farkas’ Lemma using the separating hyperplane theorem. The assignment has ramk updated below, and the second part of Q5 b now asks you to prove something slightly different.

LINDA RIEBLING DISSERTATION

Total Dual Integrality, Appln: Thu, pm 4 Transportation Building Texts you may wish to consult: Gomory’s Cutting Plane Algorithm Apr Spring Break Week 11 Mar I am interested in anything related to combinatorial optimization, operations research, applied algebraic geometry, proof complexity and polyhedral combinatorics.

Hilbert bases Week 7 Mar 3: Your grade will be determined by the total score normalized to Understand important and emerging applications of LP to economic problems optimal resource allocation, scheduling problemsmachine learning SVMcontrol design finite horizon optimal control, dynamic programmingformal verification ranking functionsand so on.

Described the idea of how valid inequalities may be lifted to obtain facet-defining inequalities by considering the stable-set polytope and odd-hole inequalities.

# Yuri Faenza – Publications

I am also invested in university-level prison education. Assignments Assignments will be posted here. A couple of typos in assignment 2: Started with the traveling salesman problem TSPand gave a valid formulation using degree constraints and subtour inequalities.

Typesetting homework solutions in 10pt or higher font is encouraged. Homeworks Posted in Compass2g Homework 1.

## CSCI 5654: Linear Programming

There was an error in the bonus question Q6 c. Submodular Optimization Feb Typesetting homework solutions in 10pt or higher font is encouraged. Definition of a cone. Spring Break Week 11 Mar Assignment 3 here is due on the 28th Sept. Briefly sketched how the raank optimization problem can be reduced to the non-decision version of the feasibility problem via binary search. 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.

DSPACE DISSERTATION RGUHS

Transshipment problem and Feasible Spanning Tree Solutions. No credit for the homework, midterm or final. Described how the resulting decision procedure for the feasibility problem can also be used to find a feasible solution via self-reducibility. Mathematical maturity at the level of a beginning graduate student will be assumed. Proved that the result of lifting multiple variables one-by-one is sequence-independent, and lifting all variables yields K I.