### CHVATAL RANK HOMEWORK

This course covered some introductory topics in combinatorics, probability, statistics, linear algebra and optimization. If you would really like some topic that is not here to be covered, come and talk to me. Lectured the first few weeks and then helped the students to choose a topic of their own to study and then advised them in their research. Matroids and examples, Matroid optimization problem Feb The following books may be used as reference books. Copies available from ECOT

Optimal allocation of resources, control design, verification, regression, relaxations of hard combinatorial problems to LP. Assignment Problem, Dynamic Programming technique, Appln: Collaboration and Cheating Policy You are allowed to collaborate on assignments unless otherwise indicated , but instances of collaboration should be within reason. Weekly homework and quizzes every other week, one midterm, one final. 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. A clarification about Q3 b in assignment 2: Stated the three basic problems of optimization, feasibility, and separation, and stated that all three are polytime equivalent.

Proved the above lemma about polyhedra. Stated the three basic problems of optimization, feasibility, and separation, and stated that all three are polytime equivalent. Math Discrete Mathematics: Due on Tue, May Lecture 9 slidesmatlab codes: Showed that the formulation with clique inequalities is stronger, and argued that the clique-inequalities are facet-defining. The first one asked students to find out about an application of multivariable calculus relevant for their future career or their interests.

Proved the equivalence of finitely generated chvztal and polyhedral cones.

## Integer Programming

Submodular Optimization Feb This course covered various topics ramk to matchings and matroids from a polyhedral perspective. Mathematical maturity at the level of a beginning graduate student will be assumed. The final grade will be determined as follows: Topics not covered in Chvatal will be covered by notes and handouts.

Redundant constraints, Dimension of polyhedron, Valid inequalities, Faces Feb 5: Posted lecture 3 slides and Handout 2. This course covered some homewogk topics in combinatorics, probability, statistics, linear algebra and optimization.

## CO452/652: Integer Programming

Defined the notion of a polytime reduction. As below with the addition of an extra-credit project where the students had to think about an advanced application of linear algebra i. Optimal allocation of resources, control design, verification, regression, relaxations of hard combinatorial problems to LP. If you would like to take the course but are unsure about the prerequisites, come and talk to me.

Solutions to Assignment 1 have been posted.

Defined separation oracle, ellipsoid, affine transformation, chhvatal the notion of volume. Showed how the full-dimensionality assumption can be dropped for an explicitly-described polyhedron K by perturbing the RHS of the constraints. Started the topic of separation vs. Assignment 4 is available updated Apr Definition of a cone.

Homeworks, Exams Midterm and Final will be in-class written exams. Also rano optimal margin classifier using SVMs not in syllabus. The students earn credits for this course through Adams State University. Started with the stable-set problem, showed the stable-set polytope is full-dimensional and gave two formulations for it.

# CO/ Integer Programming

Here are the Solutions. In Q1 cit should be “where Q is a polytope”. Electronic homewotk through email will be accepted provided it is in pdf format.

See instructor’s website Office Hours: Some of these books will be placed on reserve at the library.