Hestenes-Stiefel-Type Conjugate Direction Algorithm for Interval-Valued Multiobjective Optimization Problems

This article investigates a class of interval-valued multiobjective optimization problems (IVMOPs, in short). We define the Hestenes-Stiefel (HS, in short) 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. Moreover, we furnish several numerical examples, including convex, locally convex, and large-scale IVMOPs, to demonstrate the effectiveness of our proposed algorithm and solve them by employing MATLAB R2024a. To the best of our knowledge, the HS-type conjugate direction method has not yet been explored for the class of IVMOPs.