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Math 482 (Lecture 15): The primaldual algorithm and
applications to the shortest path algorithm II
This lecture continues discussion of Chapter 5 of the textbook (and lecture 14).
At this point, we have gone through the following iterations:
1. Given π feasible for (D) we construct a feasible point for (RP)
2. If (RP) is minimized at 0, (P) is solved
r
4. Looking at π
new
=π+θ π
r
we determine θ such that this is feasible for (D). With this new
feasible point of (D) we go back to 1 and iterate.
Question:
Why does this algorithm solve (P) (in finite time)?
Brief answer:
This is explained in Section 5.3 of the textbook.
Let me summarize the main points of the argument:
* Recall the set J of columns of A where the constraints of (D) are met with equality.
(These are called the
admissible columns
by the textbook.)
* Notice (RP) is almost the
auxiliary problem
(in the sense of phase 2 simplex) for (P).
The only difference is that we force columns NOT in J to be in the basis of the optimal
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This note was uploaded on 02/19/2012 for the course MATH 482 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff
 Math

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