CS 7301: Optimization: Linear and Integer Programming 

Instructor: R. Chandrasekaran

Office: ECSN 4.622 (Please Note: This is in the "old" building!!

Phone: (972) 883-2032 E-mail: chandra@utdallas.edu
Office Hours: W: 3:00-5:00
URL: http://www.utdallas.edu/~chandra

Teaching Assistant :  

Office: 

Office Hours:

email: 

Class Room:

Prerequisites: CS 6363 ; or consent of the instructor.

Grading Scheme

Homework and presentations (Schedule TBA)

Course Outline:

We will have class on Fridays 2:30 -- 5:15 @ ECSS 2.203

We might be able to adjust the time a little bit. We will talk about this in class.

• Introduction
• Formulations of well known problems
• Simplex Algoirthm

• Linear Algebra
• Linear Independence
• The Simplex Algorithm and Two Phases of the Simplex Method
• Simplex Algorithm in Matrix Form
• Revised Simplex Method
  • Explicit Inverse
  • Column Generation
• Sensitivity Analysis and Parametric Programming
• Bounded Variables and Separable Programming

• Duality Theory
• Algorithms Based on Duality
  • Dual Simplex
  • Self Dual
  • Primal Dual
• Linear Inequality Theory and Theorems of the Alternative
• Fourier Elimination

• Convexity
• Adjacent Vertex Methods and Fractional Programming
  • Charnes-Cooper
  • Isbell-Marlowe
  • Martos-Charnes
  • Dinkelbach-Jagannathan

• Convex Quadratic Programs and Linear Complementarity

• Network Problems and Total Unimodularity
• Large LP
  • Decomposition Principle
  • Generalized Upper Bounding

Polynomial Algorithms

• Ellipsoid Algorithm
• Ellipsoid Algorithm-I
• Interior Point Methods

Solvable Cases of Integer Programs

• Unimodular Matrices
• Matching and Local Unimodularity
• Matroids and matroid intersection
• Circular Ones and its Generalizations and Lattice Optimization
• TDI Systems: Balanced Matrices, Blocking Systems and Polyhedra, Perfect Graphs
• Nonnegative integer solutions to linear systems
• Approximations to Knapsack and Scheduling Problems.
• Hilbert Basis and its uses. 
• Pseudomatroids

• Introduction
• Lattice Basis Reduction Techniques
• Lenstra's Algorithm
• Scarf's Work
• Tardos - Frank Simultaneous Approximation
• Other Applications

Assignments

• Assignment #1
• Solution #1
• Solution #2
• Assignment #2
• Books
• Topics and Papers

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