A generalization of generalized Hukuhara Newton's method for interval-valued multiobjective optimization problems

Abstract

This article deals with a class of interval-valued multiobjective optimization problems (abbreviated as, IVMOP). We employ the notions of generalized Hukuhara (abbreviated as, gH) derivative and q-gH-Hessian to introduce the descent direction of the objective function of IVMOP at a noncritical point. Using this descent direction, we propose a new variant of Newton's method for solving IVMOP, employing an Armijo-like rule coupled with a backtracking technique to find the step length. Moreover, we establish that our proposed algorithm converges to a weak effective solution of IVMOP under certain suitable assumptions on the components of the objective function of IVMOP. A non-trivial example has been furnished to demonstrate the effectiveness of the proposed algorithm. To the best of our knowledge, this is the first time that a variant of Newton's method has been introduced to solve IVMOP, that does not involve the approach of scalarization of the objective function.