Epi-convergence in distribution of normal integrands with applications to sets of ϵ-optimal solutions
Year: 2026
Type: article
Abstract: We derive necessary and sufficient conditions for epi-convergence in distribution of normal integrands.As a basic tool for the proof a new characterisation for distributional convergence of random closed sets is used.Our approach via the epi-topology allows us to show that, if a net of normal integrands epi-converges in distribution, then the pertaining sets of ϵ-optimal solutions converge in distribution in the underlying hyperspace endowed with the upper Fell topology.Under some boundedness and uniquenss assumptions the convergence even holds for the Fell topology.Finally, measurable selections converge weakly to a Choquet-capacity.
Source: Kybernetika
Author: Dietmar Ferger
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7123700569
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