Constrained Scalar Valued Dynamic Games and Symmetric Duality for Multi Objective Variational Problem

L. Venkateswara Reddy*, Devanandam. Dola**, B. Satyanarayana***
* Professor, Department of Information Technology, Sree Vidyanikethan Engineering College (Autonomous), Tirupati, Andhra Pradesh, India.
** Lecturer and Head, Department of Mathematics, Dharma Apparao College, Nuzivid, Krishna (Dt), Andhra Pradesh, India.
*** Professor, Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Andhra Pradesh, India.
Periodicity:April - June'2018
DOI : https://doi.org/10.26634/jmat.7.2.14678

Abstract

In this paper, a certain constrained scalar valued dynamic game is formulated and shown to be equivalent to a pair of multi-objective symmetric dual variational problem. These are more generation formulations then those studied easier. Further, various duality results were obtained in this context under generalized invexity conditions.

Keywords

Scalar-Valued Game, Symmetric Duality, Generalized Invexity.

How to Cite this Article?

Reddy. L.V., Dola. D., and Satyanarayana. B. (2018). Constrained Scalar Valued Dynamic Games and Symmetric Duality for Multi Objective Variational Problem. i-manager’s Journal on Mathematics, 7(2), 17-23. https://doi.org/10.26634/jmat.7.2.14678

References

[1]. Chandra, S., Mond B., & Smart, I. (1919). Constrained games and symmetric duality with pseudo- invexity. Opsearch 1919, 27(1), 14-30.
[2]. Charnes, A. (1953). Constrained games and linear programming. Proceedings of the National Academy of Sciences. (Vol.39, No.7, pp.639-641).
[3]. Corley, H. W. (1976). Games with vector pay-offs. J. Opt. Theory Appl., 47, 491-498.
[4]. Cottle, R. W. (1963). An Infinite Game with a Convex-Concave Payoff Kernel.
[5]. Husain, I., & Ahmad, B. (2012). Constrained dynamic game and symmetric duality for variational problems. Journal of Mathematics and System Science, 2, 171-176.
[6]. Husain, I., & Jain, V. K. (2013). Constrained vector-valued dynamic game and symmetric duality for multiobjective variational problems. Open Operational Research Journal, 7, 1-10.
[7]. Kawaguchi, T., Maruyama, V. (1976). A note on mini-max (Max-min) programming. Manag Sci, 22, 670-676.
[8]. Khan, Z. A., & Hanson, M. A. (1997). On ratio invexity in mathematical programming. Journal of Mathematical Analysis and Applications, 205(2), 330-336.
[9]. Mond, B., & Weir, T. (1981). Generalized concavity and duality. Generalized Concavity in Optimization and Economics, 263-279.
[10]. Mond, B., Chandra, S., & Prasad, M. V. D. (1987). Constrained games and symmetric duality. Opsearch, 24, 69-77.
[11]. Mond, B., Hanson, M. A. (1968). Symmetric duality for variational problems. J. Math. Anal. Appl., 23(1), 161-172.
[12]. Prasad, M. D., & Sreenivas, P. C. (1997). Vector valued non zero sum games and non linear programming. Opsearch, 34(3), 180-185.
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