Nonlinear Programming

Update: August 19th, 2008

This course is intended to provide the student with the theoretical foundations of mathematical programming. The major objective of the course will be to consider a unified approach to optimization problems. The basic themes of the course are the role of duality in optimization and a unified view of algorithms for solving optimization problems. An unusual feature of the course is the development of the recent interior point techniques in mathematical programming, such as primal-dual algorithms for nonlinear programming and path following techniques. Special emphasis will also be given to applications of Nonlinear Programming in Artificial Neural Networks, Machine Learning and Data Mining. Heuristics, like tabu and scatter search will also be discussed.

Prerequisite

The minimum prerequisite for this course is a course in linear programming.

Topics

  1. Math review
  2. Convex sets
  3. Convex functions
  4. Optimality conditions
  5. Constraint qualifications
  6. Nonlinear duality
  7. Convergence
  8. Unconstrained optimization
  9. Penalty and barrier functions
  10. Feasible direction methods
  11. Interior point methods
  12. Global optimization
  13. Applications of mathematical programming

Required Text

M. S. Bazaara, H. D. Sherali and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. Wiley, 2006.

Exams and Homework

There will be one midterm and a final project. In addition, each student will be required to make an oral presentation. Several homeworks will be given during the semester. Each assignment must be turned in on time.

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