On the Integer Solution of the Hyperbolic Programming Problem
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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The problem considered is that of finding an optimal integer solution for the hyperbolic programming problem. A geometrical framework for viewing the problem is developed and a general algorithm for finding an optimal integer solution is proposed. This algorithm reduces to solving a finite sequence of linear integer programs when the number of feasible integer points is finite. It is shown that when the integer restriction is removed, the general algorithm reduces to an algorithm proposed by Isbell and Marlow to solve the continuous hyperbolic program. It is also shown that the group theoretic approach to integer programming can be used for hyperbolic integer programming. Solutions for a hyperbolic programming problems with bounded integer variables only and a hyperbolic knapsack problem are also given. It is shown that using the general algorithm to solve these problems makes it possible to reduce the number of variables at each iteration.
- Operations Research