Mapping Efficient Numerical Methods to the Solution of Multiple Objective Linear Programs.

摘要

This investigation was initiated to increase the speed, accuracy and capacity of m-simplex algorithms for solving multiple objective linear programming problems. Specifically, improvements were sought through the application of general numerical techniques. It soon became apparent that the m-simplex algorithm, like the simplex algorithm, is heavily dependent upon the technology of solving related systems of linear equations. The numerical arguments for the application of LU triangular matrix factorization techniques to simplex computations are well known. OF special significance to m-simplex performance is the case of rank-k updates to basis factorizations. A stable and efficient LU approach to the rank-k update problem is discussed. Accompanying software supports the solution of linear and transposed constructed using BLAS and Linpack libraries.