Parametric Nonlinear Programming For General Cases and Its Application to Some Problems

Abstract

This paper deals with a general nonlinear programming problem depending on a scalar parameter. Two algorithms are presented to obtain a parametric optimal solution of the problem by reducing it successively to associated problems which contain a smaller number of variables. The reduction is accomplished by partitioning variables into basic and nonbasic variables, and also by generating a reduced problem from only nonbasic variables. It is shown that both algorithms are essentially equivalent to each other. The finiteness of the algorithms is proved under certain assumptions. Application of parametric programming to handle some (originally nonparametric) problems is also indicated.