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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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. M.J. Penttinen, 2000. "Timber Harvesting with Variable Prices and Costs," Working Papers ir00045, International Institute for Applied Systems Analysis.
    7. C. Bector, 1972. "Indefinite quadratic fractional functional programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 18(1), pages 21-30, December.

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