9.16.
Do (a) - (c)
(a): No negative cycle, then flow optimal, we might need the reduced costs positive optimaity conditions?
15 Matching Annotations
- Apr 2023
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Lemma 9.14
out of kilter algorithm
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Lemma 9.13.
Out of Kilter Algorithm
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Theorem 9.5 (Weak Duality Theorem)
(9.11) is literally the dual LP formulation of the min cost flow problem onthe network.
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9.28.
This is the other way of the proof for theorem 9.4 listed earlier in the chapter.
Expression (9.8) is at page 310 for the complementary slackness conditions, expression (9.7) is page 309, thorem 9.3.
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Theorem 9.4 (Complementary Slackness Optimality Conditions)
Some flow is optimal, if and only if, there is some potential, where, the reduced costs for the potential satisfies the complementary slackness conditions for the duality of the linear program of the min cos flow problem.
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9.44.
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9.41.
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9.22.
Draw the residual graph G(x) with appropriate arc costs and the updated Residual.
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- Mar 2023
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Theorem 9.7.
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Theorem 9.6 (Strong Duality Theorem)
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Theorem 9.3 (Reduced Cost Optimality Conditions)
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Theorem 9.1
no negative cycles optimal solutions min cost flow theorem
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Theorem 9.10
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algorithm cycle-canceling
algorithm
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