### CHVATAL RANK HOMEWORK

Definition of linear and integer programs, convexity and convex hull. Homework Assignment 4 here is due on monday 5th October one week late: If you would like to take the course but are unsure about the prerequisites, come and talk to me. Simplex algorithm and its analysis, duality, complementary slackness; Geometry of linear programs; Network flow algorithms. There is no prescribed textbook for this course.

There was an error in Q5 b in assignment 2. Also discussed optimal margin classifier using SVMs not in syllabus. Assignment 6 is due on the 28th of october. Prerequisites Knowledge of linear programming at the level of CO or higher. Schrijver’s and Integer and Combinatoral Optimization: Such an acknowledgement will not incur any penalties. Started with the traveling salesman problem TSP , and gave a valid formulation using degree constraints and subtour inequalities.

Defined a decision problem, the classes P and NP, and gave some examples.

## CO452/652: Integer Programming

Tentative list of topics Some homeworrk of the following topics will be covered. Homework submision should have each problem starting in a fresh page and the submission should be stapled.

Described how one can introduce binary variables to encode whether a constraint is satisfied. Electronic submission through email will be accepted provided it is in pdf format.

## Integer Programming

Weekly homework and quizzes, one midterm, one final. Copies available from ECOT Analysis chvvatal Network Simplex Problems. Due on Thu, Feb 16 Homework 2. Homework Assignment 5 here is due on monday 12th October one week late: This course is meant to be an introduction to the basic techniques of algebra.

# Integer Optimization – Lecture Notes and Videos

This is generally a powerful tool in many research areas. You may only consult your notes and assignment solutions i.

Gave the definition of an NP-complete and NP-hard problem. Assignment Problem, Dynamic Programming technique, Appln: Started with the traveling salesman problem TSPand gave a valid formulation using degree constraints and subtour inequalities. Gave an overview of the simplex method.

# Yuri Faenza – Publications

Fundamental theorem of linear inequalities, Farkas lemma, Farkas-Weyl-Minkowski’s theorem, Caratheodary’s theorem Jan Shortest paths, Knapsack Week 12 Apr 7: This, along with the ability to encode logical statements using binary variables, gives rise to the tremendous modeling power of IPs.

Copying directly or indirectly consulting from unauthorized sources solution manuals, on line web pages, discussion forum and so on is prohibited. Grading The course will feature weekly homework assignments, and two midterm quizes. Revision of basic concepts.

Prerequisites Knowledge of linear programming ran the level of CO or higher.

Assignment Problem Apr 2: Introduction, Dual Variables, Relations between dual and primal formulations. Showed how the assumption of boundedness can be removed for polyhedra. However, you are permitted and even encouraged to discuss solution strateg ies with the instructor or other people who are enrolled in the course.

Staple and write your name in your submission. The following books may be used as reference books. Characterization of TU, Applns: Showed how the above can be applied to the BCC lift-and-project operator. Birkhoff’s theorem, Integral polyhedron, Totally Unimodular matrices Feb You are not allowed to collaborate with others or discuss your work with anyone.

Weekly homework and quizzes, one midterm, one final, two hands-on projects where the students applied what they learned to their daily lives.

Submodular Optimization Feb