Pareto efficient solution and the class of \(\alpha\)-major efficient solutions (Q1335336)

With the help of a special class of orders induced by a nonconvex cone, we introduce a class of \(\alpha\)-major efficient solutions with the parameter \(\alpha\). This is a class of solutions with respect to making various more objectives noninferior. Because of this, these solutions are better than Pareto efficient solutions. In fact, we have proved that our solutions are Pareto efficient solutions of the same problem, but the converse is not true. In addition, an important sufficient and necessary condition about the solution is given in the paper and the characteristics of the solution set are discussed. Particularly we get: when \(\alpha\leq 1\), \(\alpha\)-major efficient solutions of multiobjective convex programming are unique provided they exist.