A set relation

called lower relation

and set optimization problem and the optimal set

corresponding to the lower relation

are introduced in a partially topological linear space.Some basic properties of the optimal set are concerned.The relationship between the optimal sets of different families are investigated.The relationship between the optimal sets of a family and its subfamily are developed.Also the pertinence of the optimal sets for a family and the domination constructions is studied.The relations between the optimal sets of a family under the different domination constructions are given.A comparation is made between the conclusions in the set optimization and that in the vector optimization.