lect3 - ISE 536–Fall03 Linear Programming and Extensions...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

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.

Page1 / 4

lect3 - ISE 536–Fall03 Linear Programming and Extensions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online