IOE510+Lecture+02+08+10+Mon

IOE510+Lecture+02+08+10+Mon - IOE 510 Linear Programming I...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
1 IOE 510 Linear Programming I Monday February 8, 2010 Professor Amy Cohn
Image of page 1

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

View Full Document Right Arrow Icon
2 Announcements Exam next Monday! More info to come soon…
Image of page 2
3 Re-cap from Last Time Proved optimality of extreme points Motivating the simplex method for solving linear programs
Image of page 3

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

View Full Document Right Arrow Icon
4 Optimality of Extreme Points
Image of page 4
5 Optimal Points vs Extreme Points If a problem has an extreme point, does it have an optimal extreme point? Do unbounded problems have extreme points? Claim: If a problem has an optimal solution and has an EP , then it has an optimal EP If a problem has an EP, then it either has an optimal EP or is unbounded (i.e. has no optimal solution)
Image of page 5

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

View Full Document Right Arrow Icon
6 Algorithmic approach Enumerate all BFS’s and pick the one with the best objective value Problem 1: n-choose-m possible BFS’s Problem 2: Unbounded problems
Image of page 6
7 Degeneracy and Adjacency
Image of page 7

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

View Full Document Right Arrow Icon
8 Degeneracy A basic feasible solution is said to be degenerate if it has more than n active constraints Can these all be linearly independent? What does this look like?
Image of page 8
9 Adjacency Two basic solutions are adjacent if they share n – 1 linearly independent active constraints Two adjacent basic feasible solutions are connected by a line which is called an edge of the polyhedron
Image of page 9

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

View Full Document Right Arrow Icon
10 Optimality Conditions
Image of page 10
11 Feasible Directions
Image of page 11

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

View Full Document Right Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern