Constructive Duality for Discrete Optimization

Cover Constructive Duality for Discrete Optimization
Constructive Duality for Discrete Optimization
Marshall Lee Fisher
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After the dis- cussion of the algorithm we will give a discussion of the results of the algoritlim and their interpretation as an approximation to the optimality conditions of lemma 3. 1.
The algorithm begins with the set u, u, .. , u which is not a primitive set. A primitive set is uniquely formed by replacing u with k* the vector u where k* k Uq = max Uq .
k>m We then take the feasible basis corresponding to the first nrfl columns of A and pivot in column k*. This pivot is the ordinary simple
...x pivot. If the column of A corresponding to u is pivoted out of the starting basis then the algorithm terminates. If another column is pivoted out k* 1 of the starting basis, say column k, then the primitive set u, u, ... , u and the new basis correspond except for u and the zero column of A wtiich is still in the basis. In this case, we remove u from the primi- tive set, and replace it with a unique u e P according to lemma 6. 1. If u replaces it, then the algorithm terminates. Otherwise, the algorithm continues by repeating these same operations.

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