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An efficient algorithm for bifurcation problems of variational inequalities

Author: H. D. Mittelmann
Journal: Math. Comp. 41 (1983), 473-485
MSC: Primary 65J15; Secondary 49A29, 49D37
MathSciNet review: 717697
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Abstract: For a class of variational inequalities on a Hilbert space H bifurcating solutions exist and may be characterized as critical points of a functional with respect to the intersection of the level surfaces of another functional and a closed convex subset K of H. In a recent paper [13] we have used a gradient-projection type algorithm to obtain the solutions for discretizations of the variational inequalities. A related but Newton-based method is given here. Global and asymptotically quadratic convergence is proved. Numerical results show that it may be used very efficiently in following the bifurcating branches and that it compares favorably with several other algorithms. The method is also attractive for a class of nonlinear eigenvalue problems $ (K = H)$ for which it reduces to a generalized Rayleigh-quotient iteration. So some results are included for the path following in turning-point problems.

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Article copyright: © Copyright 1983 American Mathematical Society