An Adaptive Group Theoretic Algorithm for Integer Programming Problems

Cover An Adaptive Group Theoretic Algorithm for Integer Programming Problems
An Adaptive Group Theoretic Algorithm for Integer Programming Problems
George Anthony Gorry
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The details for making this decision are given in Section 3. 3. We will consider here the implications of the decision to find an optimal LP basis for (1. 6), on the assumption that it is not known whether group analysis with respect to this basis - 39 - has been previously performed.
Thus, let B be an optimal LP basis for (1. 6) which is found by the dual simplex method where the initial dual feasible basis is B .
If (1. 6) is an infeasible LP problem, then x is fathomed. Problem (1. 6) cannot
... have an unbounded LP solution because we assume there are upper bounds on each of the variables. Once B is found, we compare to a, t=l, ... , T. If a = a for some t, then B is not a new St St s ]^ dual feasible basis and the only recourse open is to continue x .
Suppose that o ^ o, t=l, ... , T; in this case, let B ^ = B, o = o and derive the group G, with the representation (2. 3). Solve the T+1 Unconstrained Group Problem (2. 26) for B ^ with respect to U = c k iFAJo^)f)a, , and attempt to fathom x with the tests (2.


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