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Unformatted text preview: Course website http://sites.google.com/site/kulkarniankur/teaching/fall10ge330ie310 For announcements, homeworks, lecture slides etc. Subscribe to RSS feeds https://compass.illinois.edu For grades My website (google for me) Linear Programming What does linear mean? ... In English? In Mathematics? What does programming mean? Linear function A function f is called linear if 1) f(x+y) = f(x) + f(y) for all x,y 2) f(cx) = cf(x) for all real numbers c and for all x Mathematical Programming Mathematical Programming ( Optimization ) is the study of problems that seek values to maximize or minimize objective functions under constrains. It is a primary tool of operations research. A mathematical program can be written as min(max) f ( x 1 ,x 2 , ,x n ) subject to ( x 1 ,x 2 , ,x n ) X , where x 1 ,x 2 , ,x n are the decision variables, f ( x ) is the ob jective function, and X is the set of all feasible solutions. For simplicity, sometime we stack the variables up and call it x (vec tor), i.e., x = x 1 x 2 . . . x n . 2 An Example Consider the following mathematical program. max x 1 + x 2 subject to x 1 + 2 x 2 2 2 x 1 + x 2 2 x 1 ,x 2 Notice that: the objective x 1 + x 2 is linear in x 1 and x 2 (constant weighted sum of x 1 and x 2 ); the lefthand side of the two constraints are all linear in x 1 and x 2 ; x 1 and x 2 can take any real numbers (wholenumbers or fractional values)....
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 Spring '08
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