This article investigates a class of interval-valued multiobjective optimization problems (IVMOPs). We define the Hestenes–Stiefel (HS)-type direction for the objective function of IVMOPs and establish that it has a descent property at noncritical points. An Armijo-like line search is employed to determine an appropriate step size. We present an HS-type conjugate direction algorithm for IVMOPs and establish the convergence of the sequence generated by the algorithm. We deduce that the proposed algorithm exhibits a linear order of convergence under appropriate assumptions. Moreover, we investigate the worst-case complexity of the sequence generated by the proposed algorithm. Furthermore, we furnish several numerical examples, including a large-scale IVMOP, to demonstrate the effectiveness of our proposed algorithm and solve them by employing MATLAB. To the best of our knowledge, the HS-type conjugate direction method has not yet been explored for the class of IVMOPs.

This paper deals with a class of interval-valued multiobjective optimization problems (IVMOPs). The conjugate-descent (CD) direction is defined to introduce the CD-type conjugate direction algorithm for IVMOPs. We perform the convergence analysis and establish that the algorithm exhibits a linear rate of convergence under certain suitable assumptions. We further investigate its worst-case complexity. Several numerical examples, including a large-scale problem, are provided to demonstrate the efficacy of the proposed algorithm. To the best of our knowledge, the CD-type conjugate direction algorithm is introduced for the first time to solve a class of IVMOPs.