# pdlb1 - ORIE 3300/5300 Prof. Bland Fall 2011 Motivating the...

This preview shows pages 1–2. Sign up to view the full content.

ORIE 3300/5300 Fall 2011 Prof. Bland Motivating the Primal-Dual Log Barrier Method These notes are based on lectures by Professor Michael Todd. Consider a canonical pair of primal and dual l.p. problems: max cx min yb ( P ) s.t. Ax b ( D ) s.t. yA c x 0 y 0 , where x = ( x 1 ,...,x n ) T denotes the vector of primal decision variables and y = ( y 1 ,...,y m ) denotes the vector of dual decision variables. Add slack variables s = ( s 1 ,...,s m ) T in (P) and surplus variables t = ( t 1 ,...,t n ) in (D). Now consider the optimality conditions based on part (2) of the Complementary Slackness Theorem: x is opt for ( P ) and y opt for ( D ) if s = b - Ax 0 t = yA - c 0 ( PF ) x 0 ( DF ) y 0 and t j x j = 0 j = 1 ,...,n ( CS ) y i s i = 0 i = 1 ,...,m Rather than maintaining ( PF ) and ( CS ) and working toward ( DF ), as in the simplex method, or maintaining ( DF ) and ( CS ) and working toward ( PF ), as in the dual simplex method, we will consider maintaining ( PF

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/08/2012 for the course ORIE 3300 at Cornell.

### Page1 / 2

pdlb1 - ORIE 3300/5300 Prof. Bland Fall 2011 Motivating the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online