Abstract
In this paper, the approximate efficient solution of generalized semi-infinite vector optimization problems is considered. Utilizing the density of approximate efficient points, the convexity and upper semicontinuity of constraint set mapping, we establish the connectedness of the set of approximate efficient points and the set of approximate efficient solutions to generalized semi-infinite vector optimization problems with set-valued objective maps in normed spaces. As applications, the connectedness of the solution set for semi-infinite vector optimization problems and generalized nonlinear programming problems are also obtained, respectively. Our results are new and extend the results by Gong and the results by Li.
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