Existence results for solutions of mixed tensor variational inequalities

Wenjie Mu () and Jianghua Fan ()
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Wenjie Mu: Guangxi Normal University
Jianghua Fan: Guangxi Normal University

Journal of Global Optimization, 2022, vol. 82, issue 2, No 9, 389-412

Abstract: Abstract By employing the notion of exceptional family of elements, we establish existence results for the mixed tensor variational inequalities. We show that the nonexistence of an exceptional family of elements is a sufficient condition for the solvability of mixed tensor variational inequality. For positive semidefinite mixed tensor variational inequalities, the nonexistence of an exceptional family of elements is proved to be an equivalent characterization of the nonemptiness of the solution sets. We derive several sufficient conditions of the nonemptiness and compactness of the solution sets for the mixed tensor variational inequalities with some special structured tensors. Finally, we show that the mixed tensor variational inequalities can be defined as a class of convex optimization problems.

Keywords: Mixed tensor variational inequality; Nonemptiness and compactness; Exceptional family of elements; Structured tensor; Convex analysis; 90C33; 90C30; 65H10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-021-01080-5

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