Randomized trial demonstrates contractibility of solution sets in semi-infinite optimization, suggesting new applications in vector optimization.
This paper studies contractibility of m-efficient and weak m-efficient solution sets in the context of semi-infinite set optimization with respect to a partial set order relation. Sufficient conditions for starshapedness of the image and upper semicontinuity of the constraint set map have been obtained and further employed to examine the aforementioned contractibility by way of a nonlinear scalarization function. In the end, an application to uncertain vector optimization is provided to exemplify the utility of our results.
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Upreti et al. (2025) studied this question.
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