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Characterizations and Applications of Prequasi-Invex Functions

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  • X. M. Yang
  • X. Q. Yang
  • K. L. Teo

Abstract

In this paper, two new types of generalized convex functions are introduced. They are called strictly prequasi-invex functions and semistrictly prequasi-invex functions. Note that prequasi-invexity does not imply semistrict prequasi-invexity. The characterization of prequasi-invex functions is established under the condition of lower semicontinuity, upper semicontinuity, and semistrict prequasi-invexity, respectively. Furthermore, the characterization of semistrictly prequasi-invex functions is also obtained under the condition of prequasi-invexity and lower semicontinuity, respectively. A similar result is also obtained for strictly prequasi-invex functions. It is worth noting that these characterizations reveal various interesting relationships among prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions. Finally, prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions are used in the study of optimization problems.

Suggested Citation

  • X. M. Yang & X. Q. Yang & K. L. Teo, 2001. "Characterizations and Applications of Prequasi-Invex Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 645-668, September.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:3:d:10.1023_a:1017544513305
    DOI: 10.1023/A:1017544513305
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    References listed on IDEAS

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    1. R. N. Mukherjee & L. V. Reddy, 1997. "Semicontinuity and Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 715-726, September.
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    Cited by:

    1. Y. X. Zhao & S. Y. Wang & L. Coladas Uria, 2010. "Characterizations of r-Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 186-195, April.
    2. Constantin Zălinescu, 2014. "A Critical View on Invexity," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 695-704, September.
    3. Wenyu Sun & Chengjin Li & Raimundo Sampaio, 2011. "On duality theory for non-convex semidefinite programming," Annals of Operations Research, Springer, vol. 186(1), pages 331-343, June.
    4. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.
    5. Ke Zhao & Xue Liu & Zhe Chen, 2011. "A class of r-semipreinvex functions and optimality in nonlinear programming," Journal of Global Optimization, Springer, vol. 49(1), pages 37-47, January.

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