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The Direct Power of Adjacent Vertex Programming Methods

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  • B. Martos

    (Institute of Economics of the Hungarian Academy of Sciences, Budapest)

Abstract

How far does the power of the adjacent vertex methods extend in solving non-linear programming problems? This question here gets a partial answer, being restricted to variables and objective functions which are continuous and excluding any transformation or approximation of the original system. The underlying concepts are that of quasi-concavity and quasi-monotonicity. Necessary and sufficient characteristics of the family of objective functions are given in due generality although in some cases subject to several differentiability assumptions. For these latter cases a simple criterion of vector selection is presented. Finally the problem of linear fractional programming is briefly discussed as an example.

Suggested Citation

  • B. Martos, 1965. "The Direct Power of Adjacent Vertex Programming Methods," Management Science, INFORMS, vol. 12(3), pages 241-252, November.
    • Handle: RePEc:inm:ormnsc:v:12:y:1965:i:3:p:241-252
    DOI: 10.1287/mnsc.12.3.241
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    Cited by:

    1. Frank Plastria, 2020. "On the Structure of the Weakly Efficient Set for Quasiconvex Vector Minimization," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 547-564, February.
    2. Riccardo Cambini, 1995. "Funzioni scalari affini generalizzate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 18(2), pages 153-163, September.
    3. M.J. Penttinen, 2000. "Timber Harvesting with Variable Prices and Costs," Working Papers ir00045, International Institute for Applied Systems Analysis.
    4. S. Selcuk Erenguc, 1988. "Multiproduct dynamic lot‐sizing model with coordinated replenishments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 1-22, February.
    5. Denizel, Meltem & Erenguc, Selcuk & Benson, Harold P., 1997. "Dynamic lot-sizing with setup cost reduction," European Journal of Operational Research, Elsevier, vol. 100(3), pages 537-549, August.
    6. C. Bector, 1972. "Indefinite quadratic fractional functional programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 18(1), pages 21-30, December.
    7. Timothy J. Lowe & Leroy B. Schwarz & Edward J. McGavin, 1988. "The determination of optimal base‐stock inventory policy when the costs of under‐ and oversupply are uncertain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(4), pages 539-554, August.

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