dual linear program

(definition)

Definition: Every linear program has a corresponding linear program called the dual. It is max_y{b· y | A^Ty ≤ c and y ≥ 0}. For any solution x to the original linear program and any solution y to the dual we have c · x ≥ (A^T y)^T x = y^T(Ax) ≥ y · b. For optimal x and y, equality holds. For a problem formulated as an integer linear program, a solution to the dual of a relaxation of the program can serve as witness.

Note: From Algorithms and Theory of Computation Handbook, page 34-17, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.

Author: CRC-A

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Entry modified 17 December 2004.
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Cite this as:
Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "dual linear program", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/duallinear.html