Optimization Methods
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Exams; Lecture Notes; Problem Sets
MIT OpenCourseWare details
- As taught in: Fall 2009
- Department: Sloan School of Management, Electrical Engineering and Computer Science
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Optimization methods: linear programming, duality, network flows, discrete and nonlinear optimization, interior point and semidefinite methods.
Most planning, scheduling and design problems become optimization problems once they are written down precisely. This graduate course takes a unified view of optimization, introducing the principal algorithms for linear, network, discrete, nonlinear and dynamic optimization and optimal control, with the emphasis on methodology and the mathematical structures underneath. It covers the simplex method and duality, robust optimization, network flows, branch and bound and cutting planes, optimality conditions, Newton’s method, interior point methods and semidefinite optimization.
What You Will Achieve
- Formulate applied problems as linear, discrete or nonlinear optimization models
- Solve linear programs with the simplex method and interpret duality and sensitivity
- Apply branch and bound, cutting planes and Lagrangean methods to discrete problems
- Use gradient, Newton and interior point methods for nonlinear and convex problems
Program Overview
Linear Optimization
Geometry, the simplex method and duality.
- Applications and geometry of linear optimization
- The simplex method
- Duality theory and sensitivity analysis
- Robust and large-scale optimization
Networks and Discrete Optimization
Flows and integer problems.
- Network flows
- Branch and bound and cutting planes
- Lagrangean methods, heuristics and approximation algorithms
- Dynamic programming
Nonlinear and Convex Optimization
Continuous methods beyond linear programs.
- Optimality conditions and gradient methods
- Line searches, Newton’s method and conjugate gradients
- Affine scaling and interior point methods
- Semidefinite optimization
Course Completion
Job Outlook
Optimization is used in operations research, analytics, engineering design, finance and logistics.
Good for: Graduate students in operations research, engineering or management who want a broad, rigorous optimization course.
Keep in mind: A fall 2009 course with lecture notes, problem sets and exams, and the AMPL and CPLEX student tools it points to are those of that time.
Bottom line: One course that covers the main families of optimization algorithms and the mathematics that unites them.
Frequently Asked Questions
Which software does it point to?
The AMPL student version with the CPLEX solver, with a user guide, useful directives and an AMPL tutorial listed among the tools.
Does it cover integer programming?
Yes. The discrete optimization part covers applications, branch and bound and cutting planes, Lagrangean methods, and heuristics and approximation algorithms.
How does it differ from other optimization courses?
It takes a unified view across linear, network, discrete, nonlinear and dynamic optimization, with the emphasis on methods and mathematical structure rather than on one area of application.
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