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DOI: 10.23952/cot.2026.45
Received July 18, 2025; Accepted September 10, 2025; Published online June 23, 2026
Abstract. This paper aims to study a class of mixed variational inequalities on random sets, with particular emphasis on issues pertaining to well-posedness. A central point is that the paper does not follow the standard 
framework (with 
), which has been used in previous studies and typically specializes to the case 
when presenting well-posedness results. Instead, the analysis is carried out entirely in the finer $L^\infty$ Bochner–Lebesgue space. The main contribution of the paper is a novel well-posedness result for the considered mixed random variational inequality, derived from a recent abstract stability theorem. So as another novelty of the paper, perturbations are treated not only with respect to the right-hand side given by linear random forms, but also with respect to the Carathéodory operator and the Carathéodory function, using the concept of Mosco convergence.
How to Cite this Article:
J. Gwinner, On well-posedness of mixed random variational inequalities on random sets, Commun. Optim. Theory 2026 (2026) 45.