An explicit Tikhonov algorithm for nested variational inequalities

DOI10.1007/s10589-020-00210-1zbMath1466.90112OpenAlexW3040576633MaRDI QIDQ2023653

Oliver Stein, Christoph Neumann, Lorenzo Lampariello, Simone Sagratella, Jacopo Maria Ricci

Publication date: 3 May 2021

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-020-00210-1

zbMATH Keywords

convergence rateTikhonov methodnested variational inequalitypurely hierarchical problem

Mathematics Subject Classification ID

Convex programming (90C25) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Numerical methods for variational inequalities and related problems (65K15)

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Cites Work

• Unnamed Item
• Unnamed Item
• A first order method for finding minimal norm-like solutions of convex optimization problems
• The semismooth Newton method for the solution of quasi-variational inequalities
• Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality
• Partial penalization for the solution of generalized Nash equilibrium problems
• Explicit hierarchical fixed point approach to variational inequalities
• Computing equilibria of Cournot oligopoly models with mixed-integer quantities
• On the computation of all solutions of jointly convex generalized Nash equilibrium problems
• Hybrid methods for a class of monotone variational inequalities
• Foundations of bilevel programming
• A bridge between bilevel programs and Nash games
• Algorithms for generalized potential games with mixed-integer variables
• Solving two-level variational inequality
• Numerically tractable optimistic bilevel problems
• VI-constrained hemivariational inequalities: distributed algorithms and power control in ad-hoc networks
• Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces
• Solving quasi-variational inequalities via their KKT conditions
• Computing All Solutions of Nash Equilibrium Problems with Discrete Strategy Sets
• On the solution of the KKT conditions of generalized Nash equilibrium problems
• On generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• The Standard Pessimistic Bilevel Problem
• A First Order Method for Solving Convex Bilevel Optimization Problems