Lecture11 - Advanced Operations Research Techniques IE316...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Advanced Operations Research Techniques IE316 Lecture 11 Dr. Ted Ralphs IE316 Lecture 11 1 Reading for This Lecture Bertsimas 4.1-4.3 IE316 Lecture 11 2 Duality Theory: Motivation Consider the following minimization problem minimize x 2 + y 2 s.t. x + y = 1 How could we solve this problem? Idea : Consider the function L ( x,y,p ) = x 2 + y 2 + p (1- x- y ) What can we do with this? IE316 Lecture 11 3 Lagrange Multipliers The idea is not to strictly enforce the constraints. We associated a Lagrange multiplier, or price , with each constraint. Then we allow the constraint to be violated for a price . Consider an LP in standard form. Using Lagrange multipliers, we can formulate an alternative LP: minimize c T x + p T ( b- Ax ) s.t. x How does the optimal solution of this compare to the original optimum? IE316 Lecture 11 4 Lagrange Multipliers Because we havent changed the cost of feasible solutions to the original problem, this new problem gives a lower bound ....
View Full Document

This note was uploaded on 08/06/2008 for the course IE 316 taught by Professor Ralphs during the Fall '08 term at Lehigh University .

Page1 / 14

Lecture11 - Advanced Operations Research Techniques IE316...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online