However, Method 3. In this paper, we first investigate some factors that affect the choice of r, which further determines the convergence rate. It follows from the derivatives for the variable z on both sides of equation 2. Abstract In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li Numer. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms. References J.
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An efficient implementation of the Lemke algorithm and its extension to deal with upper and lower bounds. Pages Sargent, R. W. H.. Preview Buy Chapter. Complementarity and Fixed Point Problems. Robust implementation of Lemke's method for the linear complementarity problem. Tomlin, J. A.. Pages
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Log out of ReadCube. In this paper, 2 extragradient methods for solving differential variational inequality DVI problems are presented, and the convergence conditions are derived. 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. Volume 40 , Issue The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.
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Complementarity problems were originally studied because the Karush—Kuhn—Tucker conditions in linear programming and quadratic programming constitute a linear complementarity problem LCP or a mixed complementarity problem MCP. In Lemke and Howson showed that, for two person games, computing a Nash equilibrium point is equivalent to an LCP. In Cottle and Dantzig unified linear and quadratic programming and bimatrix games.
Since then the study of complementarity problems and variational inequalities has expanded enormously. Areas of mathematics and science that contributed to the development of complementarity theory include: optimization , equilibrium problems, variational inequality theory , fixed point theory , topological degree theory and nonlinear analysis.
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