Abstract
In this paper, we provide global projection-type error bounds for general variational inequalities under certain conditions. These error bounds can be viewed as extensions of previously known results.
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NOOR, M. A., General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119-121, 1988.
PANG, J. S., and YAO, J. C., On a Generalizatioan of Normal Map and Equation, SIAM Journal on Control and Optimization, Vol. 33, pp. 168-184, 1995.
GIANNESSI, F., and MAUGERI, A., Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, NY, 1995.
HARKER, P. T., and PANG, J. S., Finite-Dimensional Variational Inequalities and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990.
ISAC, C., Complementarity Problems, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 1528, 1992.
NOOR, M. A., Some Recent Advances in Variational Inequalities, Part 1: Basic Concepts, New Zealand Journal of Mathematics, Vol. 26, pp. 53-80, 1997.
NOOR, M. A., Some Recent Advances in Variational Inequalities, Part 2: Other Concepts, New Zealand Journal of Mathematics, Vol. 26, pp. 229-255, 1997.
PANG, J. S., Error Bounds in Mathematical Programming, Mathematical Programming, Vol. 79, pp. 299-332, 1997.
PANG, J. S., A Posteriori Error Bound for the Linearly-Constrained Variational Inequality Problem, Mathematics of Operations Research, Vol. 12, pp. 474-484, 1987.
LUO, Z. Q., New Error Bounds and Their Applications to Convergence Analysis of Iterative Algorithms, Mathematical Programming, Vol. 88, pp. 341-355, 2000.
MATHIAS, R., and PANG, J. S., Error Bounds for the Linear Complementarity Problem with a P-Matrix, Linear Algebra and Applications, Vol. 132, pp. 123-136, 1990.
MANGASARIAN, O. L., and REN, J., New Improved Error Bounds for the Linear Complementary Problem, Mathematical Programming, Vol. 66, pp. 241-255, 1994.
LUO, X. D., and TSENG, P., On a Global Projection-Type Error Bound for the Linear Complementarity Problem, Linear Algebra and Applications, Vol. 253, pp. 251-278, 1997.
GOWDA, M. S., An Analysis of Zero Set and Global Error Bound Properties of a Piecewise Affine Function via Its Recession Function, SIAM Journal on Matrix Analysis, Vol. 17, pp. 594-609, 1996.
CHEN, B., and HARKER, P. T., Smooth Approximations to Nonlinear Complementarity Problems, SIAM Journal on Optimization, Vol. 7, pp. 403-420, 1997.
CHEN, B., Error Bounds for R 0?-Type and Monotone Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 108, pp. 297-316, 2001.
ZARANTONELLO, E. H., Projections on Convex Sets in Hilbert Space and Spectral Theory, Contributions to Nonlinear Functional Analysis, Edited by E. H. Zarantonello, Academic Press, New York, NY, 1971.
COTTLE, R. W., PANG, J. S., and STONE, R. E., The Linear Complementarity Problem, Academic Press, New York, NY, 1992.
PANG, J. S., and QI, L., Nonsmooth Equations: Motivation and Algorithms, SIAM Journal on Optimization, Vol. 3, pp. 443-465, 1993.
MIFFLIN, R., Semismooth and Semiconvex Functions in Constrained Optimization, SIAM Journal on Control and Optimization, Vol. 15, pp. 957-972, 1977.
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Xiu, N.H., Zhang, J.Z. Global Projection-Type Error Bounds for General Variational Inequalities. Journal of Optimization Theory and Applications 112, 213–228 (2002). https://doi.org/10.1023/A:1013056931761
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DOI: https://doi.org/10.1023/A:1013056931761