USING APPROXIMATE GRADIENTS IN DEVELOPING AN INTERACTIVE INTERIOR PRIMAL-DUAL MULTIOBJECTIVE LINEAR-PROGRAMMING ALGORITHM

We present a new interactive multiobjective linear programming algorit hm that is based on one variant of Karmarkar's algorithm known as the path-following primal-dual algorithm. The modification of this single- objective linear programming algorithm to the multiobjective case is d one by deriving an approximate gradient to the implicitly-known utilit y function. By interacting with the decision maker, locally-relevant p reference information are elicited and the approximated gradient can t herefore be continuously updated. The interior step direction is then generated by projecting the approximate gradient and taking an interio r step from the current iterate to the new one along this projection.