Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems

This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints. Under suitable constraint qualifications, we establish a necessary optimality condition for robust approximate quasi-weakly efficient solutions using the Clarke subdifferential. Subsequently, we present a sufficient optimality condition for such solutions under the assumption of approximate generalized convexity. Finally, we formulate two scalarization theorems for robust approximate quasi-weakly efficient solutions by employing a cone-strongly monotonic function. The definitions and main conclusions of this paper are supported by specific examples.