Meeting Time: First Meeting is at 218 Smith Hall on Wednesday at 3:35. But the meeting time will be changed.

Instructor: Stephan Bohacek

Email: bohacekATudel.edu

Grades will be based on homework, class participation, projects, and an exam.

Textbook: D. Bertsekas, Nonlinear Programming, Athena Scientific, 1999

Optional book: D. Luenberger, Linear and Nonlinear Programming, 1984.

Course outline

1. Introduction to optimization
1. Objective function
2. Constrained vs. unconstrained
3. Linear, quadratic, nonlinear, convex
4. Integer vs. continuous
5. Objective function (revisited)
1. Utility functions
2. Fairness
3. Convexity (accuracy of convexity)
4. Min/worst case (differentiability of min)
5. Scaled scalar
2. Linear Flow
1. Shortest path
2. Max flow
1. Linear programming
2. Complementary sensitivity (integer programming)
3. Min-cut
4. Techniques to solve max-flow
5. Multicommodity flow
6. Techniques to solve multicommodity flow
7. Related flow optimizations
8. Wireless network optimization
3. Nonlinear network optimization
   1. Motivation (bit-rate in wireless networks, utility function, min/worst case)
   2. Wired flow optimization
      1. Constrained opt
      2. Lagrange multiplier theory
      3.   Necessary and sufficient conditions for equality constraints
      4. Inequality constraints
      5. Sensitivity
      6. Duality
      7. TCP as a online solver of constrained optimization
      8. TCP modeling
   3. Wireless optimization with Lagrange multiplier methods
4. Wireless optimization (non-Lagrange multiplier methods)
1. Graph theoretic optimization
2. Maximum matching
3. Coloring
4. Maximum independent sets
5. Heuristic
6. Power control
5. Wireless MAC Modeling

Overview: This course covers contemporary optimization techniques for wired and wireless networks.