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Lecture7 - Integer Programming IE418 Lecture 7 Dr Ted...

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Integer Programming IE418 Lecture 7 Dr. Ted Ralphs
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IE418 Lecture 7 1 Reading for This Lecture Wolsey Chapter 3 Nemhauser and Wolsey Sections I.6.1, III.1.1-III.1.3
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IE418 Lecture 7 2 When is an IP Easy to Solve? We will consider an IP to be “ easy ” when we can solve all instances of it efficiently, i.e., in polynomial time. We will see that there are a number of properties that indicate an IP is easy: 1. Existence of an efficient optimization algorithm , 2. Existence of an efficient separation algorithm , 3. Existence of a complete description of the convex hull of integer solutions, 4. Existence of a certificate of optimality , or 5. Existence of a strong dual problem. We will see that under certain conditions, Properties 1 and 2 are equivalent. Property 3 implies all other properties if the description is small.
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IE418 Lecture 7 3 The Ellipsoid Algorithm The ellipsoid algorithm is an algorithm for solving linear programs.
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