Fletcher-reeves-type conjugate direction algorithm for interval-valued multiobjective optimization problems

This paper investigates a class of interval-valued multiobjective optimization problems (in short, IVMOPs). Two different Fletcher–Reeves (in short, FR)-type conjugate direction algorithms, namely, Algorithm 1 and Algorithm 2, are proposed to solve IVMOPs where the objective functions are continuously generalized Hukuhara (in short, gH) differentiable (not necessarily convex) and convex (not necessarily gH-differentiable), respectively. In Algorithm 1, the gH-derivative is used to compute FR-type directions at non-critical points, and an Armijo-like line search strategy is employed to determine appropriate step sizes along these directions. We perform the convergence analysis, establish the convergence rate, and investigate the worst-case complexity of the sequence generated by Algorithm 1, under appropriate assumptions. To develop Algorithm 2, corresponding to IVMOP, we formulate a multiobjective optimization problem (in short, MOP) and introduce an Armijo-like line search in terms of directional derivatives to compute suitable step lengths along descent directions. Finally, we establish the convergence of the sequence generated by Algorithm 2. Several nontrivial numerical examples, including a real-world application in portfolio optimization, are solved employing MATLAB R2024a to demonstrate the effectiveness of the proposed algorithms.