Skip to main content
SpringerLink
Log in

Unification and extensions of some stability theorems in mathematical programming

  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

In this paper, we provide the stability theorem for the program: inf{f(x, t)|x∈H(t)}, using the “uniformlyN-type” functions (also called ε-chainable functions[10]). This theorem generalizes the results of Dantzig[1], Hogan[2], Greenberg[3], Ying Mei-qian[4] et al.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. B. Dantzig, J. Folkman and N. Shapiro, On the Continuity of the Minimum Set of a Continuous Function,J. Maths. Anal. & Appl.,17 (1967), 519–548.

    MATH  MathSciNet  Google Scholar 

  2. W. W. Hogan, Point-to-set Maps in Mathematical Programming,Siam Review,15 (1973), 591–603.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. J. Greenberg & W. P. Pierskalla, Extensions of the Evaus-Gould Stability Theorems for Mathematical Programs,Operations Research,20: 1 (1972), 143–153.

    Article  MATH  MathSciNet  Google Scholar 

  4. Ying Mei-qian, Xu Rui-en & Wei Quan-ling, Stability of Mathematical Programming,Acta Mathematica Sinica,18: 2 (1975), 123–135.

    MATH  MathSciNet  Google Scholar 

  5. M. Avriel & I. Zang, Generalized Arcwise-connected Functions and Characterizations of Local-global Minimum Properties,J. Optimization Theory and Applications,32 (1980), 407–425.

    Article  MATH  MathSciNet  Google Scholar 

  6. Liu Guangzhong, Criteria for a Kind of Generalized Convex Functions,a Factual Profile Journal of Chengdu University of Science and Technology,4 (1984), 19–24.

    Google Scholar 

  7. Wu Fang, Yuan Yungao, Geometric Programming (I),Mathematics in Practice and Theory,1 (1982), 60–80.

    Google Scholar 

  8. C. Berge, Topological Spaces, Oliver & Boyd, 1963.

  9. M. Edelstein, Extension of Banach's Contraction Principle,Proc. Amer. Math. Soc.,12 (1961), 7–10.

    MATH  MathSciNet  Google Scholar 

  10. Thakyin Hu, Fixed Point Theorems for Multivalued Mappings,Canada Math. Bull.,23 (1980), 193–197.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Qufu Normal University, China

    Wang Changyu & Zhou Huishan

  2. Shandong Normal University, China

    Guan Meigu

Authors
  1. Wang Changyu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhou Huishan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guan Meigu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the Science Foundation of the Chinese Academy of Science.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, C., Zhou, H. & Guan, M. Unification and extensions of some stability theorems in mathematical programming. Acta Mathematicae Applicatae Sinica 5, 97–104 (1989). https://doi.org/10.1007/BF02009742

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02009742

Keywords

Search

Navigation