On conjugate direction-type method for interval-valued multiobjective quadratic optimization problems

This paper deals with a class of unconstrained interval-valued multiobjective quadratic optimization problems (in short, IVMQP) and an associated unconstrained multiobjective quadratic optimization problem (in short, MQP). Employing the relationship between the Pareto optimal solution of the associated MQP and the effective solution of IVMQP, we propose a conjugate direction-type algorithm to determine an effective solution for the IVMQP. The proposed algorithm requires a set of conjugate directions with respect to matrices corresponding to the quadratic part of the components of the objective function of MQP. In each iteration to compute the step length, we solve an unconstrained minimization problem of a single variable with a strongly convex objective function. We prove that the proposed algorithm converges to an effective solution of IVMQP in a finite number of steps under certain assumptions. Moreover, we furnish several non-trivial numerical examples to demonstrate the practical applicability and significance of the proposed algorithm.