# An Interactive Interior Point Method for Multiobjective Nonlinear Programming Problems

### Abstract

An interactive interior point algorithm for solving a multiobjective nonlinear programming problem has been proposed in this paper. The algorithm uses a single-objective nonlinear variant based on both logarithmic barrier function and Newton’s method in order to generate, at each iterate, interior search directions. New feasible points are found along these directions which will be later used for deriving bestapproximation to the gradient of the implicitly-known utility function at the current iterate. Using this approximate gradient, a single feasible interior direction for the implicitly-utility function could be found by solving a set of linear equations. It may be taken an interior step from the current iterate to the next one along this feasible direction. During the execution of the

algorithm, a sequence of interior points will be generated. It has been proved that this sequence converges to an ε − optimal solution, whereε is a predetermined error tolerance known a priori. A numerical multiobjective example is illustrated using this algorithm

**GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR)**, [S.l.], v. 2, n. 1, may 2018. ISSN 2251-3396. Available at: <http://dl6.globalstf.org/index.php/jmsor/article/view/1523>. Date accessed: 16 feb. 2019.