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Generalized arcwise-connected functions and characterizations of local-global minimum properties

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Abstract

In this paper, new classes of generalized convex functions are introduced, extending the concepts of quasi-convexity, pseudoconvexity, and their associate subclasses. Functions belonging to these classes satisfy certain local-global minimum properties. Conversely, it is shown that, under some mild regularity conditions, functions for which the local-global minimum properties hold must belong to one of the classes of functions introduced.

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References

  1. Avriel, M.,Nonlinear Programming, Analysis and Methods, Prentice Hall, Englewood Cliffs, New Jersey, 1976.

    Google Scholar 

  2. Ortega, J. M., andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.

    Google Scholar 

  3. Avriel, M., andZang, I.,Generalized Arcwise Connected Functions and Characterizations of Local-Global Minimum Properties, Tel-Aviv University, Faculty of Management, Working Paper No. 502/77, 1977.

  4. Martin, D. H.,Connected Level Sets and Uniqueness in Optimization, Part 1, National Research Institute for Mathematical Sciences, Pretoria, South Africa, CSIR Special Report No. WISK-276, 1977.

    Google Scholar 

  5. Martin, D. H.,Connected Level Sets and Uniqueness in Optimization, Part 2, National Research Institute for Mathematical Sciences, Pretoria, South Africa, CSIR Special Report No. WISK-277, 1977.

    Google Scholar 

  6. Thompson, W. A., Jr., andParke, D. W.,Some Properties of Generalized Concave Functions, Operations Research, Vol. 21, pp. 305–313, 1973.

    Google Scholar 

  7. Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.

    Google Scholar 

  8. Apostol, T. M.,Mathematical Analysis, Addison-Wesley Publishing Company, Reading, Massachusetts, 1957.

    Google Scholar 

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Author information

Author notes

  1. I. Zang (Senior Lecturer)

    Present address: Faculty of Commerce, University of British Columbia, Vancouver, British Columbia, Canada

Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, Haifa, Israel

    M. Avriel (Professor)

  2. Faculty of Management, Tel-Aviv University, Tel-Aviv, Israel

    I. Zang (Senior Lecturer)

Authors
  1. M. Avriel
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  2. I. Zang
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Additional information

Dedicated to R. Bellman

The authors are indebted to I. Kozma, N. Megiddo, and A. Tamir for valuable discussions and to S. Schaible for valuable remarks. This research was partially supported by the Fund for the Encouragement of Research at the Technion.

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Avriel, M., Zang, I. Generalized arcwise-connected functions and characterizations of local-global minimum properties. J Optim Theory Appl 32, 407–425 (1980). https://doi.org/10.1007/BF00934030

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  • DOI: https://doi.org/10.1007/BF00934030

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