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...

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Comp 360: Algorithm Design (Winter 2017) Lecture 10: LP Duality and Applications Instructor: Yang Cai Based on Kevin Wayne ’s Slides.
2 Simplex Algorithm: Corner Case Simplex algorithm. Missing details for a corner case. Q. What if min positive ratio test fails?
3 Unboundedness Q. What happens if min positive ratio test fails ? A. Unbounded objective function. all coefficients in entering column are nonpositive
LP duality Strong duality theorem Bonus proof of LP duality Applications Linear Programming II
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
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.
7 Primal problem. Idea. Add nonnegative combination ( C , H , M ) of the constraints s.t.

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