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Some Remarks On Vector Optimization Problems

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Abstract

We prove the existence of a weak minimum for vector optimization problems by means of a vector variational-like inequality and preinvex mappings.

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References

  1. Craven, B. D., Nonlinear Programming in Locally Convex Spaces, Journal of Optimization Theory and Applications, Vol. 10, pp. 197–210, 1972.

    Google Scholar 

  2. Craven, B. D., Lagrangian Conditions and Quasiduality, Bulletin of the Australian Mathematical Society, Vol. 16, pp. 325–339, 1977.

    Google Scholar 

  3. Hanson, M. A., On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 545–550, 1982.

    Google Scholar 

  4. Kuhn, H. W., and Tucker, A. W., Nonlinear Programming, Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, Edited by J. Neyman, University of California Press, Berkeley, California, pp. 481–492, 1951.

    Google Scholar 

  5. Wolfe, P., A Duality Theorem for Nonlinear Programming, Quarterly of Applied Mathematics, Vol. 19, pp. 239–244, 1961.

    Google Scholar 

  6. Craven, B. D., and Glover, B. M., Invex Functions and Duality, Journal of the Australian Mathematical Society, Vol. 39A, pp. 1–20, 1985.

    Google Scholar 

  7. Weir, T., and Jeyakumar, V., A Class of Nonconvex Functions and Mathematical Programming, Bulletin of the Australian Mathematical Society, Vol. 38, pp. 177–189, 1988.

    Google Scholar 

  8. Kaul, R. N., and Kaur, S., Sufficient Optimality Conditions Using Generalized Convex Functions, Opsearch, Vol. 19, pp. 212–224, 1982.

    Google Scholar 

  9. Fan, K., A Generalization of Tychonoff's Fixed-Point Theorem, Mathematics Annals, Vol. 142, pp. 305–310, 1961.

    Google Scholar 

  10. Chen, G. Y., Existence of Solutions for a Vector Variational Inequality: An Extension of the Hartmann-Stampacchia Theorem, Journal of Optimization Theory and Applications, Vol. 74. pp. 445–456, 1992.

    Google Scholar 

  11. Chen, G. Y., and Craven, B. D., Existence and Continuity for Vector Optimization, Journal of Optimization Theory and Applications, Vol. 181, pp. 459–468, 1994.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, India

    K. R. Kazmi (Lecturer) & K. R. Kazmi (Lecturer)

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  1. K. R. Kazmi
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Kazmi, K.R. Some Remarks On Vector Optimization Problems. Journal of Optimization Theory and Applications 96, 133–138 (1998). https://doi.org/10.1023/A:1022667201624

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