An explicit Tikhonov algorithm for nested variational inequalities

Lorenzo Lampariello (), Christoph Neumann, Jacopo M. Ricci, Simone Sagratella and Oliver Stein
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Lorenzo Lampariello: Roma Tre University
Christoph Neumann: Karlsruhe Institute of Technology (KIT)
Jacopo M. Ricci: Roma Tre University
Simone Sagratella: Sapienza University of Rome
Oliver Stein: Karlsruhe Institute of Technology (KIT)

Computational Optimization and Applications, 2020, vol. 77, issue 2, No 1, 335-350

Abstract: Abstract We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We give conditions that guarantee the convergence of the proposed method. Moreover, inspired by recent works in the literature, we provide a convergence rate analysis. In particular, for the simple bilevel instance, we are able to obtain enhanced convergence results.

Keywords: Nested variational inequality; Purely hierarchical problem; Tikhonov method; Convergence rate; 90C33; 90C25; 90C30; 65K15; 65K10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-020-00210-1

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