A logarithmic barrier function method for solving nonlinear multiobjective programming problems

Abstract: An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton method for determining Newton’s directions along which line searches are performed. It also has been proved that the number of iterations required by the suggested algorithm to converge to an ε-optimal solution is O(m |ln ε|), depending on predetermined error tolerance ε and the number of constraints m.