On the solution of monotone nested variational inequalities

Lorenzo Lampariello (), Gianluca Priori () and Simone Sagratella ()
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Lorenzo Lampariello: Roma Tre University
Gianluca Priori: Sapienza University of Rome
Simone Sagratella: Sapienza University of Rome

Mathematical Methods of Operations Research, 2022, vol. 96, issue 3, No 4, 446 pages

Abstract: Abstract We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in the literature to guarantee the convergence to solutions of the nested variational inequality. Specifically, we only need monotonicity of the upper- and the lower-level variational inequalities. Also, we provide the first complexity analysis for nested variational inequalities considering optimality of both the upper- and lower-level.

Keywords: Nested variational inequality; Purely hierarchical problem; Tikhonov method; Complexity analysis; 90C33; 90C25; 90C30; 65K15; 65K10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00186-022-00799-5

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