I.E. 2081: NONLINEAR OPTIMIZATION

INSTRUCTOR:

Prof. Jayant Rajgopal
1032 Benedum Hall
Tel. No.: 412-624-9840
e-mail: rajgopal@pitt.edu

PREREQUISITES:

  1. Differential calculus
  2. Vectors, matrices and linear algebra
  3. Familiarity with basic concepts from real analysis such as sets, functions, continuity, etc.
  4. An interest in mathematical methods!

TEXT:

There is no required text. Copies of detailed lecture notes which will be made available for download from this web page; students are expected to make use of the library to supplement these notes. For those who would like to buy a text, the following is highly recommended: Linear and Nonlinear Optimization by Griva, Nash and Sofer, SIAM Press, Philadelphia, Second edition (2009).

NOTES:

Module 1
Module 2
Module 3
Module 4
Module 5
Module 6

REFERENCES:

Other good references - several of these are on reserve in the library (in addition to the text):
  1. Nonlinear Programming: Theory and Algorithms; by Bazaraa, Sherali and Shetty
  2. Nonlinear Programming: Analysis and Methods- Avriel
  3. Practical Optimization - Gill, Murray and Wright
  4. Foundations of Optimization - Beightler, Phillips and Wilde
  5. Introduction to Linear and Nonlinear Programming - Luenberger
  6. Numerical Optimization Techniques - Evtushenko
  7. Numerical Optimization - Nocedal and Wright
  8. Nonlinear Programming - Bertsekas

COURSE OUTLINE:

This course is aimed at upper level graduate students in Engineering, Operations Research, Management Science, Applied Mathematics, Computer Science and Economics. The objective is to expose the student to different types of nonlinear programming problems, and to the various algorithms used to solve these. While requisite theory will be covered, the emphasis of the course is neither on formal theorems and proofs, nor on specific applications, but rather, on structure and methods. Topics to be covered include (tentatively) solution of simultaneous nonlinear equations; unconstrained optimization of single and multiple variable functions by both derivative and derivative-free methods, including search methods, conjugate gradient and variable metric algorithms; necessary conditions for optimality; convexity and convex programming; constrained optimization including penalty and barrier function methods, Lagrangian algorithms, and primal methods; Lagrangian duality; quadratic, fractional, separable and geometric programming; computer packages to solve NLP problems. Other topics might be added or some of the above topics might be left out, depending on time constraints and class interests.

GRADING:

Primarily on the basis of two examinations. Homework assignments and a paper/project might account for a small portion of the grade.

HOMEWORK ASSIGNMENTS:

Homework 1  (Solutions)
Homework 2  (Solutions)
Homework 3
Homework 4
Homework 5
Homework 6

Geometric Programming Software:

Right click on the link to download the file GPINSTAL.zip and then save it to you own drive/device.  Extract the program (gpglp.exe), support program (dosxmsf.exe), parameter file (parms.pos), documentation (GPGLP-manual.*) and three sample data files along with the output from the optimal solutions.  Read the documentation to learn how to use the program.
Here is a zip file with GGPLAB (for MATLAB).