# lect1 - ISE 536–Fall03 Linear Programming and Extensions...

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

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.

Unformatted text preview: ISE 536–Fall03: Linear Programming and Extensions August 27, 2003 Lecture 1: Introduction to Linear Programming Lecturer: Fernando Ord´ o˜nez 1 Course Organization Instructor: Fernando Ord´ o˜nez GER-247, x1-2413 [email protected] Office hours: 1:00-3:00 p.m. on Thursdays Assignments: Almost weekly problem sets. Handed out on Mondays, due the following Monday at the beginning of class. No late assignments. A random subset of problems will be graded. Some computational problems to be carried out with NEOS Server (http://www- neos.mcs.anl.gov/). More explanation in time. Grades: Will be determined from homework average, two midterms and final with the following weights: homework: 30%, each midterm: 20%, and final: 30%. Course Text: Dimitri Bertsimas and John Tsitsiklis, Introduction to Linear Optimization , Athena Scientific, 1997. Course webpage: http://www-rcf.usc.edu/˜fordon/LP, and Blackboard: (http://learn.usc.edu/) 1 2 Introduction to Linear Programming Linear Programming (LP) is a special class of problems within optimization problems: min / max f ( x ) s . t . x ∈ S . • x is the decision variable • f ( ) is the objective function • S is the constraint set For an LP • x ∈ < n • f ( x ) = c t x = ∑ n i =1 c i x i • The set S is defined by linear constraints: S = { x ∈ < n | a t i x ≤ b i ,i = 1 ,...,m 1 , a t i x = b i ,i = m 1 +1 ,...,m 2 , a t i x ≥ b i ,i = m 2 +1 ,...,m } A function is linear if • f ( αx ) = αf ( x ) • f ( x + y ) = f ( x ) + f ( y ) Show that for a linear function f (0) = 0....
View Full 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 / 8

lect1 - ISE 536–Fall03 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