# lect11 - ISE 536Fall03 Linear Programming and Extensions...

This preview shows pages 1–3. Sign up to view the full content.

ISE 536–Fall03: Linear Programming and Extensions October 6, 2003 Lecture 11: Duality, Introduction Lecturer: Fernando Ord´o˜nez 1 Deﬁnition Here the rows of the matrix A are a t i , for i = 1 ,...,m , and the columns are A j , j = 1 ,...,n . For any linear programming problem: ( P ) min c t x s . t . a t i x = b i i M 1 a t i x b i i M 2 a t i x b i i M 3 x j 0 j N 1 x j 0 j N 2 x j unbounded j N 3 there exists a closely related LP problem called the dual: ( D ) max y t b s . t . y t A j c j j N 1 y t A j c j j N 2 y t A j = c j j N 3 y i unbounded i M 1 y i 0 i M 2 y i 0 i M 3 1

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

View Full Document
For example, construct the dual of the problem ( P ) min 2 x 1 + x 2 s . t . - x 1 + 3 x 2 = 5 2 x 1 + 7 x 2 3 x 1 1 x 1 0 x 2 unrestricted 2 Relation between ( P ) and ( D ) In matrix notation we have that ( P ) min c t x s . t . Ax = b x 0 then ( D ) max y t b s . t . y t A c t This dual problem is sometimes expressed in the more symmetric form
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/13/2012 for the course ISE 536 taught by Professor Yy during the Spring '05 term at South Carolina.

### Page1 / 4

lect11 - ISE 536Fall03 Linear Programming and Extensions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online