Based on the semiinvex convex function proposed by DUTTA J， the ψstrong semiinvex convex function is given for the equivalence form of the approximate solution sets of the convex optimization problems. The properties of quasioptimal solution sets of the singleobjective optimization problems are showed by ηsubdifferential and ηnormal cone. Furthermore， the equivalence form of the quasioptimal solution sets of the singleobjective optimization problems is thus obtained.