Skip to main content
Log in

Characterizations of semi-prequasi-invexity

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Because of its importance in optimization theory, the concept of convexity has been generalized in various ways. With these generalizations, to seek some practical criteria for them is especially important. In this paper, some criteria are developed for semi-prequasi-invexity, which includes prequasi-invexity as the special case. Mutual characterizations among semi-prequasi-invex functions, strictly semi-prequasi-invex functions, and strongly semi-prequasi-invex functions are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Similar content being viewed by others

References

  1. Martin D H, The essence of invexity, Journal of Optimization Theory and Applications, 1985, 47(1): 65–76.

    Article  MathSciNet  MATH  Google Scholar 

  2. Ben-Israel A and Mond B, What is invexity? The Journal of the Australian Mathematical Society, Series B, 1986, 28(1): 1–9.

    Article  MathSciNet  MATH  Google Scholar 

  3. Noor M A and Noor K I, Some characterizations of strongly preinvex functions, Journal of Mathematical Analysis and Applications, 2006, 316(2): 697–706.

    Article  MathSciNet  MATH  Google Scholar 

  4. Fan L and Guo Y, On strongly α-preinvex functions, Journal of Mathematical Analysis and Applications, 2007, 330(2): 1412–1425.

    Article  MathSciNet  MATH  Google Scholar 

  5. Yang X M and Li D, On properties of preinvex functions, Journal of Mathematical Analysis and Applications, 2001, 256(1): 229–241.

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang X M, Yang X Q, and Teo K L, Characterizations and applications of prequasi-invex functions, Journal of Optimization Theory and Applications, 2001, 110(3): 645–668.

    Article  MathSciNet  MATH  Google Scholar 

  7. Luo H Z and Xu Z K, On characterizations of prequasi-invex functions, Journal of Optimization Theory and Applications, 2004, 120(2): 429–439.

    Article  MathSciNet  MATH  Google Scholar 

  8. Antczak T, (p, r)-invex sets and functions, Journal of Mathematical Analysis and Applications, 2001, 263(2): 355–379.

    Article  MathSciNet  MATH  Google Scholar 

  9. Anderson G D, Vamanamurthy M K, and Vuorinen M, Generalized convexity and inequalities, Journal of Mathematical Analysis and Applications, 2007, 335(2): 1294–1308.

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen X, Some properties of semi-E-convex functions, Journal of Mathematical Analysis and Applications, 2002, 275(1): 251–262.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mukherjee R N and Keddy L V, Semicontinuity and quasiconvex functions, Journal of Optimization Theory and Applications, 1997, 94(3): 715–720.

    Article  MathSciNet  MATH  Google Scholar 

  12. Mohan S R and Neogy S K, On invex sets and preinvex functions, Journal of Mathematical Analysis and Applications, 1995, 189(3): 901–908.

    Article  MathSciNet  MATH  Google Scholar 

  13. Yang X M and Li D, Semistrictly preinvex functions, Journal of Mathematical Analysis and Applications, 2001, 258(1): 287–308.

    Article  MathSciNet  MATH  Google Scholar 

  14. Luo H Z and Wu H X, On the relationships between G-preinvex functions and semistrictly G-preinvex functions, Journal of Computational and Applied Mathematics, 2008, 222(2): 372–380.

    Article  MathSciNet  MATH  Google Scholar 

  15. Craven B D, Characterizing invex and related properties, Eberhard A, Hafjusavvas N, and Luc D T, (eds.): Generalized Convexity, Generalized Monotonicity and Applications, Springer, New York, 2005, 77: 183–191.

    Chapter  Google Scholar 

  16. Ruiz-Garzón G, Osuna-Gómez R, and Rufián-Lizana A, Generalized invex monotonicity, European Journal of Operational Research, 2003, 144(3): 501–512.

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhao Y X, Wang S Y, and Coladas Uria L, Characterizations of r-convex functions, Journal of Optimization Theory and Applications, 2010, 145(1): 186–195.

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang X M, Semi-preinvexity and multi-objective programming problems, Journal of Chongqing Normal University (Edition of Natural Science), 1994, 11(1): 1–5 (in Chinese).

    MATH  Google Scholar 

  19. Yang X M and Liu S Y, Note three kinds of generalized convexity, Journal of Optimization Theory and Applications, 1995, 86(2): 501–513.

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang X M, Yang X Q, and Teo K L, Criteria for generalized invex monotonicities, European Journal of Operational Research, 2005, 164(1): 115–119.

    Article  MathSciNet  MATH  Google Scholar 

  21. Avriel M, Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, 1976 (in Chinese).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yingxue Zhao.

Additional information

This research was supported partially by the National Natural Science Foundation of China under Grant Nos. 71101088, 71003057, 71171129, the National Social Science Foundation of China under Grant No. 11&ZD169, the Shanghai Municipal Natural Science Foundation under Grant Nos. 10ZR1413200, 10190502500, 11510501900, 12ZR1412800, the China Postdoctoral Science Foundation under Grant Nos. 2011M500077, 2012T50442, the Science Foundation of Ministry of Education of China under Grant No. 10YJC630087, and the Doctoral Fund of Ministry of Education of China under Grant No. 20113121120002.

This paper was recommended for publication by Editor DAI Yuhong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, Y., Meng, X., Qiao, H. et al. Characterizations of semi-prequasi-invexity. J Syst Sci Complex 27, 1008–1026 (2014). https://doi.org/10.1007/s11424-014-1109-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-014-1109-1

Keywords

Navigation