论文信息 - On Quasimonotone Variational Inequalities

On Quasimonotone Variational Inequalities

In this paper, we study variational inequalities with multivalued mappings. By employing Fan's lemma, we establish the existence result for the dual formulation of variational inequalities with semistrictly quasimonotone mappings. We also show that similar results for quasimonotone variational inequalities do not hold.

I. V. Konnov | I. Konnov

[1] K. Fan. A generalization of Tychonoff's fixed point theorem , 1961 .

[2] G. Minty. Monotone (nonlinear) operators in Hilbert space , 1962 .

[3] D. Kinderlehrer,et al. An introduction to variational inequalities and their applications , 1980 .

[4] P. Panagiotopoulos. Inequality problems in mechanics and applications , 1985 .

[5] Mau-Hsiang Shih,et al. Browder-Hartman-Stampacchia variational inequalities for multi-valued monotone operators☆ , 1988 .

[6] Patrick T. Harker,et al. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[7] Siegfried Schaible,et al. On strong pseudomonotonicity and (semi)strict quasimonotonicity , 1993 .

[8] Jen-Chih Yao,et al. Multi-valued variational inequalities with K-pseudomonotone operators , 1994 .

[9] Anatoly Antipin. The convergence of proximal methods to fixed points of extremal mappings and estimates of their rate of convergence , 1995 .

[10] I. V. Konnov. A general approach to finding stationary points and the solution of related problems , 1996 .

[11] Siegfried Schaible,et al. Quasimonotone variational inequalities in Banach spaces , 1996 .