On the nonemptiness and boundedness of solution sets for weakly homogeneous vector optimization problems

Weakly homogeneous vector optimization is a class of nonconvex vector optimization problems.Based on the asymptotic cone and asymptotic function,strong and weak regularity conditions for weakly homogeneous vector optimization problem are given,and their properties are discussed.Under the regularity conditions,the nonemptiness and boundedness of (weakly) Pareto efficient solution set for weakly homogeneous vector optimization problems are studied.Furthermore,a new sufficient condition for the nonemptiness and boundedness of the solution set is proposed, and its relationship with the strong regular condition is discussed.