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Unformatted text preview: Multiperiod Planning Soft Constraints Goal Programming IE426: Optimization Models and Applications: Lecture 9 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University September 26, 2006 Jeff Linderoth IE426:Lecture 9 Multiperiod Planning Soft Constraints Goal Programming Quiz #1 Closed Book, Closed Notes. 75 minutes. (It took me 31 minutes to take the quiz). 4 problems: 1 Short Answer (35%) , 3 modeling. Jeff Linderoth IE426:Lecture 9 Multiperiod Planning Soft Constraints Goal Programming Convexity How to tell if a function is convex/concave... Line over/under test. Examine the Hessian (matrix of 2nd partial derivatives). If numerical, I will only ask you for simple functions, in which x R 2 How to tell if a set is convex Line inside test How to use this information about region shape to know whether a problem is easy or hard. Jeff Linderoth IE426:Lecture 9 Multiperiod Planning Soft Constraints Goal Programming Other Things LP Graphing feasible regions Solving LPs by graphing Properties of LP solution Optimal solution occurs at an extreme point!Optimal solution occurs at an extreme point!...
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 Spring '08
 Linderoth
 Optimization

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