Connectedness of Strong Efficient Solution Set for Set-valued Optimization Problems under Condition of Cone-convexlike with Constraints

Set-valued optimization problem is one of the main research fields of vector optimization theory and applications. One of the important research subjects of set-valued optimization problem is to investigate the connectedness properties of the solution set, as it provides a possibility moving from one solution to other solution. In this paper, we present the theorem of the connectedness of strong efficient solution set for set-valued optimization problems in the local convex spaces. The theorem is proved under the condition that the domain is a nonempty compact set and the objective mapping is a cone-convexlike and the constraint mapping is upper semi-continuous set-valued. The obtained theorem in this paper extends the relative results about the connectedness of the strong efficient solution set of vector optimization with set-valued maps.