An interactive interior point algorithm for multiobjective linear programming problems

We propose an interactive interior point method for finding the best compromise solution to a multiple objective linear programming problem. We construct a sequence X⁰,X1,...,X^k,... of smaller and smaller polytopes which shrink towards the compromise solution. During the kth interation, we move from the center of polytope X^k−1 to the center of polytope X^k by performing a local optimization which consists of maximizing a linear function over an ellipsoid.