Effective Solution of Non-Convex Multi-Objective Ratio Goals Problems

摘要

Multiple ratio goals often occur in equity considerations and imply non-linear non-convex programming problems. Charnes and Cooper's solution of such a class by a sequence of linear programs is herein implemented by an effective computational method applicable to a larger class of non-linear non-convex problems. An analytical prescription of the recursion to preserve feasibility of the last basic solution is derived. A new usage of the fast re-inversion routine of current LP codes to obtain the modified basis inverse is developed together with the further subroutines of the Opposite Sign Algorithm of Charnes and Kortanek (1963) or a negative image scheme whenever the old basic solution is not basic feasible for the modified problem. An illustration in terms of funding of State colleges in Texas is provided. (Author)