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Arcwise Connected Cone-Convex Functions and Mathematical Programming

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Abstract

The concept of arcwise connected cone-convex functions in topological vector spaces is introduced. Optimality conditions and duality theorems for a vector-valued nonlinear programming problem involving arcwise connected cone-convex functions are discussed.

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References

  1. Avriel, M., and Zang, I., Generalized Arcwise Connected Functions and Characterization of Local-Global Minimum Properties, Journal of Optimization Theory and Applications, Vol. 32, pp. 407-425, 1980.

    Google Scholar 

  2. Singh, G., Elementary Properties of Arcwise Connected Sets and Functions, Journal of Optimization Theory and Applications, Vol. 41, pp. 377-387, 1983.

    Google Scholar 

  3. Mukherjee, R. N., and Yadav, S.R., A Note on Arcwise Connected Sets and Functions, Bulletin of the Australian Mathematical Society, Vol. 31, pp. 369-375, 1985.

    Google Scholar 

  4. Bhatia, D., and Mehra, A., Optimality Conditions and Duality Involving Arcwise Connected and Generalized Arcwise Connected Functions, Journal of Optimization Theory and Applications, Vol. 100, pp. 181-194, 1999.

    Google Scholar 

  5. 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 

  6. Weir, T., Mond, B., and Craven, B.D., Weak Minimization and Duality, Numerical Functional Analysis and Optimization, Vol. 9, pp. 181-192, 1987.

    Google Scholar 

  7. Kuhn, H. W., and Tucker, A.W., Nonlinear Programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Edited by J. Neuman, University of California Press, Berkeley, California, pp. 481-492, 1951.

    Google Scholar 

  8. Abadie, J., On the Kuhn-Tucker Theorem, Nonlinear Programming, Edited by J. Abadie, North-Holland, Amsterdam, Netherlands, pp. 19-36, 1967.

    Google Scholar 

  9. Jahn, J., Mathematical Vector Optimization in Partially-Ordered Linear Spaces, Verlag Peter Lang, Frankfurt am Main, Germany, 1986.

    Google Scholar 

  10. Hayashi, M., and Komiya, H., Perfect Duality for Convexlike Programs, Journal of Optimization Theory and Applications, Vol. 38, pp. 179-189, 1982.

    Google Scholar 

  11. Jeyakumar, V., Convexlike Alternative Theorems and Mathematical Programming, Optimization, Vol. 16, pp. 643-652, 1985.

    Google Scholar 

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Fu, J., Wang, Y. Arcwise Connected Cone-Convex Functions and Mathematical Programming. Journal of Optimization Theory and Applications 118, 339–352 (2003). https://doi.org/10.1023/A:1025451422581

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  • DOI: https://doi.org/10.1023/A:1025451422581

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