NIST

dual linear program

(definition)

Definition: Every linear program has a corresponding linear program called the dual. It is maxy{b· y | ATy ≤ c and y ≥ 0}. For any solution x to the original linear program and any solution y to the dual we have c · x ≥ (AT y)T x = yT(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


Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.
HTML page formatted Fri Feb 23 10:06:07 2018.

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