Lecture4 - Advanced Operations Research Techniques IE316...

Info iconThis preview shows pages 1–5. 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
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 4 Dr. Ted Ralphs IE316 Lecture 4 1 Reading for This Lecture • Bertsimas 2.2-2.4 IE316 Lecture 4 2 The Two Crude Petroleum Example Revisited • Recall the Two Crude Petroleum example. • We showed graphically that the optimal solution was an extreme point . • How did we figure out the coordinates of the optimal point? IE316 Lecture 4 3 Binding Constraints Consider a polyhedron P = { x ∈ R n | Ax ≥ b } . Definition 1. If a vector ˆ x satisfies a T i ˆ x = b i , then we say the corresponding constraint is binding . Theorem 1. Let ˆ x ∈ R n be given and let I = { i | a T i ˆ x = b i } represent the set of constraints that are binding at ˆ x . Then the following are equivalent: • There exist n vectors in the set { a i | i ∈ I } that are linearly independent. • The span of the vectors { a i | i ∈ I } is R n . • The system of equations a T i x = b i ,i ∈ I,x ∈ R n has the unique solution ˆ x . If the vectors { a j | j ∈ J } for some J ⊆ [1 ,m ] are linearly independent, we will say that the corresponding constraints are also linearly independent. IE316 Lecture 4...
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

Lecture4 - Advanced Operations Research Techniques IE316...

This preview shows document pages 1 - 5. Sign up to view the full document.

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