### 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

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