Spring 2004
A convex function to be optimized. (Graph courtesy of Prof. Robert Freund.)
Course Highlights
Nonlinear Programming features videos of three key lectures in their entirety. A set of comprehensive lecture notes are also available, which explains concepts with the help of equations and sample exercises.
Course Description
This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interiorpoint algorithms and theory, Lagrangian relaxation, generalized programming, and semidefinite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interiorpoint methods and penalty and barrier methods.
Special Features
Technical Requirements
Special software is required to use some of the files in this course: .rm.
*Some translations represent previous versions of courses.
Syllabus
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This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interiorpoint algorithms and theory, Lagrangean relaxation, generalized programming, and semidefinite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interiorpoint methods and penalty and barrier methods.
Required Text
Bertsekas, Dimitri P. Nonlinear Programming. 2nd ed. Athena Scientific Press, 1999. ISBN: 1886529000.
Recommended Alternate Text
Bazaraa, Mokhtar S., Hanif D. Sherali, and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. New York: John Wiley & Sons, 1993. ISBN: 0471557935.
Course Requirements
 Weekly Problem Sets (about 12).
 Midterm Examination (inclass, closed book).
 Final Examination (3hour exam).
 Computer Exercises.
Grading
Grading will be based on the following:

Calendar

Readings
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Bertsekas, Dimitri P. Nonlinear Programming. 2nd ed. Athena Scientific Press, 1999. ISBN: 1886529000.
Recommended Alternate Text
Bazaraa, Mokhtar S., Hanif D. Sherali, and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. New York: John Wiley & Sons, 1993. ISBN: 0471557935.
Background Reading in Linear Programming and Real Analysis
Linear Programming
For those students who have not had any exposure to linear programming, it is recommended that you read the following sections from one of the following two texts:
Luenberger, David G. Linear and Nonlinear Programming. 2nd ed. Reading, MA: Addison Wesley, 1984. ISBN: 0201157942.
 Chapter 2: Sections 2.12.5
 Chapter 3: Sections 3.13.5, 3.7
 Chapter 4: Sections 4.14.4
Or: Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization. Athena Scientific Press, 1997. ISBN: 1886529191.
 Chapter 1: Sections 1.1, 1.2, 1.4
 Chapter 2: Sections 2.1, 2.2
 Chapter 3: Sections 3.1, 3.2, 3.5
 Chapter 4: Sections 4.1, 4.2, 4.3
Analysis
For those students who have not had any exposure to real analysis, you should read the following sections of the text:
Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. McGrawHill, 1976. ISBN: 007054235X.
 Chapter 2: pp. 2443 (the whole chapter)
 Chapter 3: pp. 4761
 Chapter 4: pp. 8395
Lecture Notes

Recitations
Note that there were no recitations during the weeks of the midterm exam (week 7), spring break (week 8), or Sloan Innovation Period (week 9).

Exams
This course includes a closedbook midterm exam, held during lecture 13 for 90 minutes, and a threehour final exam, given after the course has finished. A sample midterm, used in the 1998 version of this course, is available.
Midterm Exam (PDF)
Video Lectures
RealOne™ Player software is required to run the .rm files in this section.
The three video lectures available below illustrate the content and teaching style of this course.

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