Premium
Extragradient methods for differential variational inequality problems and linear complementarity systems
Author(s) -
Fatemi S. Z.,
Shamsi M.,
Bozorgnia Farid
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4523
Subject(s) - mathematics , variational inequality , lipschitz continuity , complementarity (molecular biology) , complementarity theory , convergence (economics) , differential inclusion , mixed complementarity problem , constant (computer programming) , upper and lower bounds , mathematical optimization , mathematical analysis , nonlinear system , computer science , genetics , physics , quantum mechanics , economics , biology , programming language , economic growth
In this paper, 2 extragradient methods for solving differential variational inequality (DVI) problems are presented, and the convergence conditions are derived. It is shown that the presented extragradient methods have weaker convergence conditions in comparison with the basic fixed‐point algorithm for solving DVIs. Then the linear complementarity systems, as an important and practical special case of DVIs, are considered, and the convergence conditions of the presented extragradient methods are adapted for them. In addition, an upper bound for the Lipschitz constant of linear complementarity systems is introduced. This upper bound can be used for adjusting the parameters of the extragradient methods, to accelerate the convergence speed. Finally, 4 illustrative examples are considered to support the theoretical results.