Methods of parametric non-linear programming

Abstract

This paper deals with general parametric non-linear programming problems. First, two algorithms are presented to obtain a parametric optimal solution of the problem having a single parameter by reducing it successively to associated problems which contain a smaller number of variables. The reduction is accomplished by partitioning the variables into basic and non-basic, and also by generating a smaller problem from the non-basic variables only. It is shown that the two algorithms are essentially equivalent to each other. Next, this idea is extended to handle a certain class of multi-parametric problems. Finally, computational results of the algorithm are given.