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Unformatted text preview: ISE 536–Fall03: Linear Programming and Extensions September 3, 2003 Lecture 3: Geometry, Basic Feasible Solutions Lecturer: Fernando Ord´ o˜nez 1 Examples of LP Geometry Let us construct examples of LPs which have • bounded feasible region and single solution • bounded feasible region and multiple solutions • unbounded feasible region and multiple solutions • unbounded feasible region and unbounded objective function value • infeasible feasible region Optimum seems to be always in a “corner”. In this class we will make this precise. 1 1.1 Effects of Transformation on the Geometry Consider the problem min z = x 1 x 2 s . t . x 1 + x 2 ≤ 1 x 1 ,x 2 ≥ Always have the same general shape? 2 Notation • Polyhedron: P = { x ∈ < n  Ax ≤ b } • Polytope: A bounded polyhedron. • S is a convex set iff for all x,y ∈ S and any λ ∈ [0 , 1], λx + (1 λ ) y ∈ S ....
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This note was uploaded on 02/13/2012 for the course ISE 536 taught by Professor Yy during the Spring '05 term at South Carolina.
 Spring '05
 YY

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