lecture2 - Class Information Modeling Class Information...

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Class Information Modeling IE426: Optimization Models and Applications: Lecture 2 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University August 31, 2006 Jeff Linderoth IE426:Lecture 2 Class Information Modeling Nitty Gritty Details Course Overview Today’s Outline Newcomers? (Survey/Say Cheese!) Review Optimization Problems Objective Functions Constraint Classifications Linear Programming Jeff Linderoth IE426:Lecture 2 Class Information Modeling Nitty Gritty Details Course Overview Please don’t call on me!!! 1 Name one reason we would want to build an optimization model. 2 What is the different between an optimization model and an optimization instance? 3 What is my son’s name? :-) Jeff Linderoth IE426:Lecture 2 Class Information Modeling Nitty Gritty Details Course Overview General Optimization Model max x R n f ( x ) subject to g i ( x ) = b i i M x X x is an n-dimensional vector : x = ( x 1 , x 2 , . . . , x n ) . f ( x ) : Objective Function M : Constraint Set g i ( x ) {≤ , = , ≥} b i : Constraint X : Explicit Constraint Set Jeff Linderoth IE426:Lecture 2
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Class Information Modeling Nitty Gritty Details Course Overview Fancy Math Notation means “for all” means “in” R : Set of real numbers Z : Set of integers R n : Set of real valued n -dimensional vectors R n + : Set of real valued, non-negative, n -dimensional vectors Z n × m : Set of all integer-valued m × n matrices Jeff Linderoth IE426:Lecture 2 Class Information Modeling Nitty Gritty Details Course Overview The Joy of Sets Get used to it! Summing over sets will be a common operation in this class S = { 1 , 2 , 3 } , T = { R , G } x Z | S | y R | S |×| T | i S x i def = x 1 + x 2 + x 3 i S j T y ij def = y 1 , R + y 1 , G + y 2 , R + y 2 , G + y 3 , R + y 3 , G k T a k x k def = a R x R + a G x G Jeff Linderoth IE426:Lecture 2 Class Information Modeling Nitty Gritty Details Course Overview An Optimization Instance minimize sin( x ) subject to 4 x 2 16 ( c 1 ) x {- 2 , - 1 , 0 , 1 , 2 } x is a vector of dimension 1.
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