IOE 611
Nonlinear Programming


Instructor: Professor Katta G. Murty, 232 IOE Bldg., 763-3513,

Prerequisites: A course in linear programming, equivalent to IOE 510.

Course objectives: To expose the student to nonlinear models, their applications, how to construct them, and to algorithms for solving them satisfactorily


  1. M.S. Bazaraa, H.D. Sherali, and C.M. Shetty, Nonlinear Programming Theory and Algorithms, Wiley, 1993, 2nd Edition.
  2. K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Helderman-Verlag, 1988.(This book is now available for download).
  3. R. Fletcher, Practical Methods of Optimization, Wiley-Interscience, 1987.


  1. Formulation of continuous optimization models, curve fitting, parameter estimation, L_1 and L_2 and L_infty-measures of deviation. Difference between linear and nonlinear model building. Examples.
  2. Types of problems. State of the art. What can and cannot be done efficiently? Goals for algorithms.
  3. Theorems of alternatives for linear systems.
  4. Convex sets, separating hyperplanes, convex and concave functions.
  5. Optimality conditions.
  6. Quadratic programming and complementary pivot methods.
  7. Newton's method and simplicial methods for nonlinear equations.
  8. Line Search methods.
  9. Unconstrained minimization algorithms.
  10. Constrained minimization algorithms. Penalty and barrier methods, SQP and SLP methods.

Work in the course: Homeworks every week. One midterm and final. A computer project.

Lecture Notes (Transparencies):

611 syllabus
Introduction Pages 1 to 17
Formulation examples Pages 18-28
Goals for algorithms Pages 29-31
Fundamental concepts Pages 32-35
Theorems of alternatives Pages 36-44
Separating hyperplanes Pages 45-48
Convex functions Pages 49-50
Opt. conds. for NLP Pages 51-70
QP and LCP Pages 71-77
Line search algorithms Pages 78-90
Nonlinear equations Pages 91-95
Unconstrained min algos. Pages 96-109
Linear Equality constrained min Pages 110-113
Linearly constrained min Pages 114-126
Nonlinear constraints Pages 127-147