Biproportional Matrix Balancing with Upper Bounds

  • Heinz Spiess
Part of the Applied Optimization book series (APOP, volume 63)


The purpose of the note is to look at the problem of biproportional matrix balancing when upper bounds are imposed on the matrix elements. This problem can be formulated as a convex minimization problem. Using the Kuhn-Tucker optimality conditions the functional form of the resulting model is derived. The dual formulation of the problem is derived and it is shown how it can be solved by a cyclic coordinate descent method. This leads to the proposal of an efficient solution algorithm.


Dual Problem Dual Variable Dual Formulation Convex Minimization Problem Coordinate Descent Method 
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© Springer Science+Business Media Dordrecht 2002

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  • Heinz Spiess

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