A unified feasible direction interior approach to the minimization of linear and general objective functions subject to linear constraints

Abstract

A modification of Snyman's interior feasible direction method for linear programming is proposed and the method is also extended to problems where the objective function is non-linear. The method attempts to identify the optimal bounding set of active constraints. In the modified algorithm the successive interior steps in the identifying cycle are no longer constrained to be in the place of constant objective function value, but are computed to ensure improvement in the objective function for any non-zero step taken within the cycle. The method is also extended to non-linear objective functions by allowing for line searches within the interior and along bounding hypersurfaces. A formal unified algorithm is presented and the method is illustrated by its successful application to a number of simple problems from different categories.