On the complexity of solving feasible linear programs specified with approximate data

The problem of solving linear programs specified with approximate data is considered. Algorithms are given for linear programs having both general inequality and nonnegativity constraints and for linear programs having only general inequality constraints. Given approximate data for the actual (unknown) instance, the algorithms use knowledge that the instance in question is primal feasible to reduce the data precision necessary to give an approximation to the solution set of the actual instance when the actual instance has an optimal solution. In some cases, problem instances that would otherwise require perfect precision to solve can now be solved with approximate data because of the knowledge of primal feasibility. The algorithms are computationally efficient. Furthermore, the algorithms require not much more data accuracy than the minimum amount necessary to give an approximate solution of a desired accuracy when the actual instance has an optimal solution. This work aids in the development of a computational complexity theory that uses approximate data and knowledge.