{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

affinescaling_slides - ALGORITHMS FOR LP PROBLEMS I 1 2 3 4...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
ALGORITHMS FOR LP PROBLEMS I 1 Simplex Method - Dantzig 1947. 2 Affine Scaling Method - Dikin 1967 3 Ellipsoidal Method (Polynomial time algorithm)- Kachian 1979. 4 Projective Transformation Method (Polynomial time algorithm) - Karmarkar 1984. 5 Path Following Method (Polynomial time algorithm)- Various 1986. Saigal (U of M) IOE 310 1 / 8
Image of page 1

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

View Full Document Right Arrow Icon
INTERIOR POINT METHOD: THE FORM OF LP I Consider the following linear programming problem in standard form: minimize n j =1 c j x j n j =1 a i , j x j = b i i = 1 , · · · , m x j 0 j = 1 , · · · , n and assume that it has an interior point solution x 0 1 > 0, x 0 2 > 0, · · · , x 0 n > 0 . Also, the lp in matrix form: minimize c T x Ax = b x 0 Saigal (U of M) IOE 310 2 / 8
Image of page 2
INTERIOR POINT METHOD: THE FORM OF LP II Given the interior point x 0 , define the diagonal matrix D = x 0 1 x 0 2 . . . x 0 n . As an example, consider the following linear program: minimize 6 x 1 - 2 x 2 + x 3 x 1 + 2 x 2 - 3 x 3 + x 4 = 1 x 2 - x 3 + x 4 = 1 x 1 0 x 2 0 x 3 0 x 4 0 Saigal (U of M) IOE 310 3 / 8
Image of page 3

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

View Full Document Right Arrow Icon
INTERIOR POINT METHOD: THE FORM OF LP III with the interior point x 0 1 = 1, x 0 2 = 1, x 0 3 = 1, x 0 4 = 1 . Note that A = 1 2 - 3 1 0 1 - 1 1 , c = 6 - 2 1 0 , b = 1 1
Image of page 4
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
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