A family of convolutions of the vector criterion for finding points in the Pareto set

A family of convolutions of the vector criterion into a scalar one are discussed that satisfy the irredundancy and sufficiency requirements. If the criteria are continuous functions one closed limited search region then the family is applicable for designing a finite $\varepsilon$-network for the Pareto set in the criterion space. If, additionally, the search region is convex and the criteria are stringently quasiconvex functions, then the set is useful for design of a finite $\varepsilon$-network for the Pareto network in the parameter space.