On an interconnection between the Lipschitz continuity of the solution map and the positive principal minor property in linear complementarity problems over Euclidean Jordan algebras

In the setting of Euclidean Jordan algebras, we study the Lipschitz continuity of the solution map of linear complementarity problems. We show that if the solution map is Lipschitz continuous and if the linear transformation has the Q-property, then the linear transformation has the positive principal minor property.