Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data

In this article, a mathematical programming problem under affinely parameterized uncertain data with multiple objective functions given by SOS-convex polynomials, denoting by (UMP), is considered; moreover, its robust counterpart, denoting by (RMP), is proposed by following the robust optimization approach (worst-case approach). Then, by employing the well-known $$\epsilon $$ ϵ -constraint method (a scalarization technique), we substitute (RMP) by a class of scalar problems. Under some suitable conditions, a zero duality gap result, between each scalar problem and its relaxation problems, is established; moreover, the relationship of their solutions is also discussed. As a consequence, we observe that finding robust efficient solutions to (UMP) is tractable by such a scalarization method. Finally, a nontrivial numerical example is designed to show how to find robust efficient solutions to (UMP) by applying our results.