AUXILIARY PROBLEM PRINCIPLE EXTENDED TO MONOTONE VARIATIONAL INEQUALITIES

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AKHTAR A. KHAN

Abstract




In the present work, the use of the operator method of regularization in the sense of Tikhonov, which makes it possible to develop an iterative scheme via auxiliary problem principle, converging strongly towards the solution of multi- valued monotone variational inequality within the absence of strong monotonicity condition of involved operator, is sustained.




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KHAN, A. A. (1996). AUXILIARY PROBLEM PRINCIPLE EXTENDED TO MONOTONE VARIATIONAL INEQUALITIES. Tamkang Journal of Mathematics, 27(2), 117–124. https://doi.org/10.5556/j.tkjm.27.1996.4349
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Papers

References

C. Baiocchi and A. Capelo, "Variational and quasi-variational inequalities, applications to free boundary value problems", Wiley, New York, 1984.

A. B. Bakushinsky, "Methods for solving monotone variational inequalities based on the iterative regularization principle," USSR Comp. Maths. Math. Phy., 17(1977), 1350-1362.

A. B. Bakshinsky and B. T . Poljak, "On the solution of variational inequalities," Soviet Math. Dok/., 15(1974), 1705-1710.

F. E. Browder, "On the unificaiton of the calculus of variations and the theory of monotone non- linear operators in Banach spaces," Proc. Nat. Acad. Sci. USA, 56(1966), 419-425.

F. E. Browder, " Existence and approximation of solution of nonlinear variational inequalities," 56(1966), 1080-1086.

G. Cohen, Auxiliary problem principle extended to variational inequalities,JOTA, 59(1988), 325- 333.

S. Dafermos, "Traffic equilibria and variational inequalities," Trans. Sci., 14(1980), 42-54.

G. Duvaut and J. L. Lions, " Les inequations in mechanique et en physique,"Dunod-Paris, 1972 (Eng. Tran., Springer, Berlin, 1976).

I. Ekeland and R. Temam "Analyse convex et problems variationallles," Dunod-Paris, 1974 (Eng. Tran., North Holland, Amsterdam, 1970).

R. Glowinski J. L. Lions and R, Tremolires "Analyse numerique des inequations variationnelles (Tome 1 et 2), Dunod," Paris(Eng. Tran., North Holland, Amsterdam, 1981).

G. Isac "Tikhonov's regularization and the complementarity problem in Hilbert spaces," J. Math. Anal. Appl., 174(1993), 53-66.

L. D. Muu, "An augumented penalty function method for solving a class of variational inequalities," USSR Comp. Maths. Math. Phy., 26(1986), 117-122.

M. A. Noor, "On nonlinear variational inequalities," Inter. J.Math. & Math. Sci., 14(1991), 399-402.

R. Saigal,"Extension of the generalized complementarity problem," Math. Oper. Res., 1(1976), 260-266.

A. N. Tikhonov and V. Y. Arsenin, "Solution of ill posed problems," J.Wiley sons, New York, 1977.