On approximate solutions for linear fractional optimization problems on Euclidean Jordan algebras

This research delves into the study approximate optimality conditions for approximate solutions to a linear fractional optimization problem over symmetric cone defined on a Euclidean Jordan algebras. Without the presence of constraint qualifications, it provides approximate optimality conditions expressed by sequences. The paper shows also that this result yields the approximate optimality condition for the linear fractional optimization problem under a suitable constraint qualification. Moreover, related dual models in both sequential approximate form and approximate form are formulated, and then, approximate weak duality and approximate strong duality assertions are proposed. Besides, in accordance with the fulfilment of constraint qualification, approximate converse duality assertion is also established. At last, relation between approximate solutions to a linear fractional optimization problem over symmetric cone and approximate solutions to a linear optimization problem over symmetric cone is investigated. Some examples are given to illustrate the significance of our obtained results.