Nonlinear Programming
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Lecture Notes; Lecture Videos
MIT OpenCourseWare details
- As taught in: Spring 2004
- Department: Sloan School of Management, Electrical Engineering and Computer Science
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Nonlinear optimization theory and methods: optimality conditions, Newton’s method, interior-point and barrier methods, duality and semidefinite programming.
The fundamentals of nonlinear optimization theory and methods are the subject of this class, which covers unconstrained and constrained optimization, Lagrange and conic duality, and semidefinite programming. Algorithms studied include steepest descent, Newton’s method, subgradient optimization, and interior-point, penalty and barrier methods. Lecture videos and notes follow each topic through optimality conditions, theory and practice.
What You Will Achieve
- State optimality conditions for constrained and unconstrained problems
- Apply Newton’s method and steepest descent
- Use penalty, barrier and interior-point methods
- Derive duals and analyze semidefinite optimization problems
Program Overview
Unconstrained Optimization
The opening lectures build conditions and basic methods.
- Optimality conditions
- Newton’s method
- Quadratic forms
- Steepest descent method
Constrained Optimization
The next lectures add constraints and algorithms for them.
- Constrained optimality conditions
- Projection and penalty methods
- Barrier methods
- Interior-point methods
Convexity and Duality
The final lectures cover the theory.
- Analysis of convex sets and functions
- Duality theory
- Subgradient optimization
- Semidefinite optimization
Course Completion
Job Outlook
Optimization methods like these are used across operations research, engineering and quantitative management.
Good for: Graduate students in operations research, engineering and related fields who want a thorough theoretical course on nonlinear optimization.
Keep in mind: Materials are lecture videos and notes plus one sample midterm from 1998, so you will not find the weekly problem sets or computer exercises. Bertsekas’s textbook is required and not supplied.
Bottom line: A lecture-based treatment of optimization theory, to pair with practice problems from the textbook.
Frequently Asked Questions
What are the set and alternate texts?
Nonlinear Programming by Dimitri P. Bertsekas, 2nd edition, is the required text, and Nonlinear Programming: Theory and Algorithms by Bazaraa, Sherali and Shetty is the recommended alternate.
Is a practice exam available?
Yes. A sample midterm from the 1998 version is available. The class held a closed-book midterm for 90 minutes and a three-hour final exam.
How much of it covers duality?
Four lectures are devoted to duality theory, after two on the analysis of convex sets and functions, and three more cover semidefinite optimization.
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