(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
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 17 December 2004.
HTML page formatted Mon Feb 2 13:10:39 2015.
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: http://www.nist.gov/dads/HTML/duallinear.html