IJPAM: Volume 119, No. 2 (2018)

Title

A NUMERICAL APPROACH FOR GENERALIZED
VARIATIONAL-LIKE INEQUALITY PROBLEMS

Authors

S.N. Mishra$^1$, P.K. Das$^2$, G.C. Nayak$^3$
$^{1,2}$Department of Mathematics
School of Applied Sciences
KIIT Deemed to be University
Bhubaneswar, 751024, INDIA
$^3$Department of Mathematics
Govt. Junior College, Phulbani
Kandhmala, 762001, INDIA

Abstract

A pair of generalized variational-like inequality problems ([*]) and its corresponding dual variational-like inequality problems ([*]) are defined. The equivalence theorem of the problems ([*]) and ([*]) is studied using the concept of affineness in the first quadrant of a unit circle via a transformation $T^*$. Again a pair of generalized complementarity-like problems and its dual complementarity problems are defined. The existence of their solutions are shown in the presence of the problems ([*]) and ([*]). A numerical study of the problems ([*]) has been undertaken in $\eta$-invex set using auxiliary principle technique.

History

Received: August 20, 2018
Revised: June 22, 2018
Published: June 23, 2018

AMS Classification, Key Words

AMS Subject Classification: 65K10, 90C33, 47J30
Key Words and Phrases: Invex set, affineness on the circle, generalized variational-like inequality problems, generalized dual variational-like inequality problems, generalized complementarity - like problems, generalized dual complementarity - like problems, auxiliary principle technique

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Bibliography

1
A. Behera and P.K Das. Variational Inequality Problems in $H$-spaces, International Journal of Mathematics and Mathematical Sciences, Article ID 78545: 1 - 18, 2006.

2
B. D. Craven, Invex Function and Constrained Local Minima, Bulletin of Australian Mathematical Society, 24 (1981), 357 - 366.

3
P. K. Das: An iterative method for $T$-$\eta$-invex function in Hilbert space and Coincidence Lifting Index Theorem for Lifting Function and Covering Maps,Advances in Nonlinear Variational Inequalities, 13 (2) (2010), 11 - 36.

4
R. Glowinski, J. L. Lions and R. Tremolieres, Numerical Analysis of variational inequalities, North-Holland Amsterdam, Holland (1981).

5
M. A. Hanson, On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, 80 (1981), 545 - 550.

6
T. Weir and B. Mond, Pre-invex functions in multiple objective optimizaton, J. Math. Anal. Appl., 136 (1988), 29 - 38.

7
G. Stampacchia: Formes bilineaires coercivities sur les ensembles convexes, C. R. Acad. Sci. Paris, 258 (1964), 4413 - 4416.

How to Cite?

DOI: 10.12732/ijpam.v119i2.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 2
Pages: 281 - 293


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