Lecture 10 LP Duality and Applications.pdf - Comp 360 Algorithm Design(Winter 2017 Lecture 10 LP Duality and Applications Instructor Yang Cai Based on

Lecture 10 LP Duality and Applications.pdf - Comp 360...

This preview shows page 1 - 8 out of 14 pages.

Comp 360: Algorithm Design (Winter 2017) Lecture 10: LP Duality and Applications Instructor: Yang Cai Based on Kevin Wayne ’s Slides.
Image of page 1
2 Simplex Algorithm: Corner Case Simplex algorithm. Missing details for a corner case. Q. What if min positive ratio test fails?
Image of page 2
3 Unboundedness Q. What happens if min positive ratio test fails ? A. Unbounded objective function. all coefficients in entering column are nonpositive
Image of page 3
LP duality Strong duality theorem Bonus proof of LP duality Applications Linear Programming II
Image of page 4
5 LP Duality Primal problem. Goal. Find an upper bound on optimal value. Ex 1. Multiply 2 nd inequality by 6 : 24 A + 24 B 960. z * = 13 A + 23 B 24 A + 24 B 960. objective function
Image of page 5
6 LP Duality Primal problem. Goal. Find an upper bound on optimal value. Ex 2. 1 st inequality: 5 A + 15 B 480. Multiply 2 nd inequality by 2 : 8 A + 8 B 320. z * = 13 A + 23 B = (5 A + 15 B) + ( 8 A + 8 B) 800.
Image of page 6
7 Primal problem. Idea. Add nonnegative combination ( C , H , M ) of the constraints s.t.
Image of page 7
Image of page 8

You've reached the end of your free preview.

Want to read all 14 pages?

  • Winter '13
  • AdrianRoshanVetta

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

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors