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Unformatted text preview: IE 495 – Stochastic Programming Problem Set #2 Due Date: February 26, 2003 Do all three of the following problems. If you work alone, you will receive a 10% bonus on your score. You are allowed to examine outside sources, but you must cite any references that you use. Please don’t discuss the problems with other members of the class (other than your partner, if you are working with one). 1 Math Time 1.1 Problem Birge and Louveaux #4, Page 102. Interlude You will need to know the following stuff to answer problem #2. 1 Definition A function f : D ( f ) 7→ R ( f ) is Lipschitz continuous on its domain D ( f ) if and only if there exists a constant L (called the Lipschitz constant) such that | f ( a )- f ( b ) | ≤ L | a- b | for all a,b ∈ D ( f ) 2 Definition The left-derivative of a function f : < 7→ < is the quantity f- ( x ) = lim x → t- f ( x )- f ( t ) x- t = sup x<t f ( x )- f ( t ) x- t . 3 Definition The right-derivative of a function f : < 7→ < is the quantity f + ( x ) = lim x → t + f ( x )- f ( t ) x- t = inf x>t f ( x )- f ( t ) x- t ....
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- Spring '08
- Continuous function, Lipschitz, additional capacity