Abstract
In questo lavoro si estende il concetto di funzione affine a tutte le classi di funzioni che verificano sia una sorta di concavità generalizzata sia la corrispondente proprietà di convessità generalizzata. Di tali classi vengono studiate le relazioni di inclusione e le proprietà relative alle trasformazioni di funzione.
Summary
In this paper some different classes of functions, generalizing the concept of affine function, are introduced and studied. Properties and relationships among the classes are given and some properties about functions transformation are provided.
Bibliografia
Arrow, K. J., Enthoven, A. C.,Quasi-concave programming, Econometrica, 29, 1961, 779–800.
Avriel M.,Nonlinear programming: analysis and methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1976.
Avriel M., Diewert W. E., et al.,Generalized concavity, Mathematical concepts and methods in science and engineering 36, edited by A. Miele, Plenum Press, New York, 1988.
Cambini A. Martein L.,A modified version of Martos's Algorithm, Methods of Operation Research, 53, 1986, 33–44.
Cambini A., Martein L.,Equivalence in linear fractional programming, Optimization, 23, 1992, 41–51.
Cambini R.,A class of non-linear programs: theoretical and algorithmical results, in Generalized Convexity, edited by S. Komlósi, T. Rapcsák, and S. Schaible, Springer-Verlag, 1994, 294–310.
Cambini R. Nuove classi di funzioni scalari concave generalizzate, Rivista di Matematica per le Scienze Economiche e Sociali, 1, 1994, 1–18.
Charnes A., Cooper W. W.,Programming with linear fractional functionals, Naval Research Logistics Quarterly, 19, 1962, 181–186.
Chew K. L., Choo E. U.,Pseudolinearity and Efficiency, Mathematical Programming, 28, 1984, 226–239.
Diewert W. E., Avriel M. Zang I. Nine kinds of quasiconcavity and concavity, J. Econ. Theory, 25, 1981, 397–420.
Hirche J. Optimizing of sums and products of linear fractional functions under linear constraints, Technical report n. 3, Fachbereich Mathematik und Informatik, Martin Luther Universitat, Halle-Wittenberg, Halle, Germany, 1995.
Karamardian S.,Duality in mathematical programming. J. Math. Anal. Appl., 20, 1967, 344–358.
Kornbluth S. H., Steuer R. E.,Multiple Objective Linear Fractional Programming, Management Science, 27, 1981, 1024–1039.
Kortanek K. O., Evans J. P.,Pseudo-concave programming and Lagrange regularity, Operations Research, 15, 1967, 882–891.
Mangasarian O. L.,Nonlinear programming, McGraw-Hill, New York, 1969.
Martos B.,Hyperbolic Programming, Naval Research Logistic Quarterly, 11, 1964, 135–155.
Martos B. The direct power of adjacent vertex programming methods, Manage. Sci., 12, 1965, 241–252.
Martos B.,Quasi-convexity and quasi-monotonicity in nonlinear programming, Studia Sci. Math. Hung., 2, 1967, 265–273.
Martos B.,Nonlinear programming: theory and methods, North-Holland, Amsterdam, 1975.
Ortega J. M., Rheinboldt W. C.,Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970.
Stoer J., Witzgall C.,Convexity and optimization in finite dimensions, Springer-Verlag, Berlin, 1970.
Thompson W. A., Parke D. W.,Some properties of generalized concave functions, Operation Research, 21, 1973, 305–313.
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Cambini, R. Funzioni scalari affini generalizzate. Rivista di Matematica per le Scienze Economiche e Sociali 18, 153–163 (1995). https://doi.org/10.1007/BF02096425
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DOI: https://doi.org/10.1007/BF02096425