Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Multiplier Vector

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200502

For a given feasible basis B to a linear-programming problem, let the row vector cB be the ordered set of cost coefficients for the vectors in B. The multiplier vector is defined as π = cBB−1. If B is an optimal basis, then the components of π are the dual variables associated with the corresponding primal constraints. The vector π is also called the simplex multiplier vector, with the components of π being the simplex multipliers.


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