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STOR 415 Handout
Duality
The dual LP
Each LP is paired with another LP. One in this pair is called the primal
problem, and the other is called the dual. Given the primal problem, one
can ﬁnd the dual problem by following the procedure below.
1. For each constraint of the primal, deﬁne a dual variable
•
Sign restrictions will be treated diﬀerently; do not deﬁne variables
for them
2. Determine the dual objective function
•
If the primal is a max problem, then the dual is a min problem.
Conversely, if the primal is a min problem, then the dual is a max
problem.
•
Use the righthand sides of the primal constraints as coeﬃcients
in the dual objective function
3. Determine data in the dual constraints
•
Coeﬃcients of the variables in the dual constraints are coeﬃcients
of the variables in the primal constraints, but transposed
•
Righthand sides of the dual constraints are coeﬃcients in the
primal objective function
4. Determine types of the dual constraints
•
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This note was uploaded on 05/10/2011 for the course STOR 415 taught by Professor Shulu during the Spring '11 term at University of North Carolina School of the Arts.
 Spring '11
 ShuLu

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