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

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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....
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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.

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

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