Subham Poddar

In this paper, using the properties of Clarke subdifferential, we derive some characterizations of locally Lipschitz geodesic pseudolinear functions on Hadamard manifolds. Moreover, employing these characterizations, we derive some properties of the solution sets of pseudolinear programming problems on the Hadamard manifold. The results established in this paper generalize and extend several known results in the literature. We furnish several examples to illustrate these results. Furthermore, to demonstrate the practical applications of our outcomes, we solve a specific form of the Karcher mean problem by employing the results established in this paper.

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.