A new scheme for approximating the weakly efficient solution set of vector rational optimization problems

In this paper, we provide a new scheme for approximating the weakly efficient solution set class of vector optimization problems with rational objectives over feasible defined by finitely many polynomial inequalities. More precisely, present procedure to obtain sequence explicit approximations problem in question. Each approximation is intersection sublevel single and set. To end, make use achievement function associated considered construct it from above. Remarkably, construction can be converted semidefinite programming problems. Several nontrivial examples are designed illustrate proposed scheme.