Characterizations of locally Lipschitz Geodesic pseudolinear functions on Hadamard manifolds

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Abstract
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.

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