# CHVATAL RANK HOMEWORK

Faces, Facets Week 4 Feb 7: Homeworks, Exams We will have 4 homeworks and 2 exams. Due on Tue, May 2. Prior coursework in Linear Programming and Graph Theory will be helpful. Showed how the assumption of boundedness can be removed for polyhedra. 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.

Polyhedron, Decomposition theorem for polyhedron, Polytopes Week 3 Feb 3: Matroids and examples, Matroid optimization problem Feb Definition of a cone. Collaboration and Cheating Policy You are allowed to collaborate on assignments unless otherwise indicated , but instances of collaboration should be within reason. 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. Familiarity with reading and writing mathematical proofs and basic knowledge in Linear Algebra are required. Week 1 Jan

Shortest Path Problem Mar Tue, 11am-noonTransportation Building Teaching Assistant: Described and analyzed the Ellipsoid method assuming the underlying set K is closed, convex, contained in a bounding ball, and contains a ball.

Dimension of polyhedron, Redundant constraints, Valid inequalities Feb 2: Showed how maintaining lower and upper bounds in the BnB method can enable one to prune portions of the BnB tree and avoid complete enumeration. Week 1 Jan Chvatal Rank of rational polyhedron Apr Started the topic of separation vs.

THESIS DUNNOTTAR FUND

## CO452/652: Integer Programming

Started with computational complexity. Polytopes, faces, dimension of polyhedra Integral polyhedra: Typesetting homework solutions in 10pt or higher font is encouraged.

Weekly homework, four midterms, one final, two hands-on projects where the students applied what they learned to their daily lives. National Math Festival in Washington D.

# Integer Optimization – Lecture Notes and Videos

This class is taught through University Beyond Barsan organization providing higher education to people in prisons. This class was taught chcatal 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.

Started with lift-and-project operators.

This course will cover the theory of integer programming, which has its roots in elegant polyhedral theory and duality, its applicability in modeling optimization problems, and algorithms for solving integer programs.

Solutions will be due before the beginning of the lecture. Matroids and examples, Matroid optimization problem Feb Solutions will be due on the Thursday of the nomework week before the beginning of the lecture.

# CO/ Integer Programming

Defined fixed-charge flow problems. Defined affine independence, dimension of a set.

DE LA SALLE ZOBEL NOTES AND HOMEWORK

You may only consult your notes and assignment solutions i. Here are the Solutions. 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.

Future – You can find me at the following seminars, conferences and workshops: The assignment has been updated below, and the second part of Q5 b now asks you to prove something slightly different. Due on Tue, Apr 11 Homework 4.

## CSCI 5654: Linear Programming

Email submissions will NOT be accepted. Due on April 3, Total Dual Integrality, Applns: At the end of the course, the successful student will be able to cast various problems that may arise in her research as optimization problems, cyvatal the cases where the optimization problem will be linear, choose appropriate solution methods and interpret results appropriately.

This course was meant to teach students the foundational ranj needed for higher mathematics and a language for understanding the principles of science, engineering, economics, etc. Proved the above lemma about polyhedra. Showed how the assumption of boundedness can be removed for polyhedra.