Lecture06 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis Kara Lecture # 6 Date: 7 October 2007 1
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2 Some Conventions
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Geometric Solutions Revisited Recall the LP models with 2 variables The optimum solution was an extreme point. How do we find the coordinates of an extreme point? 3
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EXTREME POINTS A point x in a convex set S , is called an extreme point of S if x cannot be represented as a strict convex combination of two distinct points of S . In other words if and 1) 0 ( with ) 1 ( 2 1 x x x S , 2 1 x x 2 1 x then x x 4
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Extreme Points Ex: Given a convex set S x 1 x 3 x 2 5
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Binding Constraints Consider If a vector x satisfies we say that the corresponding constraint is active or binding at x. } : { b Ax R x P n i T i b x a 6
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Let be a polyhedron. Let x Є R n . The vector x is a basic solution with respect to P if there exists n linearly independent and binding constraints at x. If x is a
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Lecture06 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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