Abstract
This paper aims to review the main lines of development for parametric analysis conducted in a qualitative way to state properties of monotonicity and concavity in the classical and generalized framework.
Some fields, in which this approach reveals to be particularly useful are then presented. *** DIRECT SUPPORT *** A00BX008 00003
Riassunto
Il lavoro presenta le principali linee di sviluppo per l'analisi parametrica condotta con strumenti qualitativi per stabilire proprietà di monotonia e concavità classiche e generalizzate.
Per i diversi tipi di problemi si mette in evidenza l'utilizzo illustrando alcune applicazioni.
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References
Bector C. R., Cambini A., Fractional programming—some recent results, in [3], Springer Verlag, 1990, 86–98.
Bonnans J. F., Shapiro A., Optimization problems with perturbations: a guided tour, Siam Review, 40(2), 1998, 228–264.
Cambini A., Castagnoli E., Martein L., Mazzoleni P., Schaible S., (eds.) Generalized Convexity and Fractional Programming with Economic Applications, Springer Verlag, 1990.
Castagnoli E., Mazzoleni P.,Verso un unico tipo di concavità, Rivista di Matematica per le Scienze Economiche e Sociali, 9(1), 1986a, 15–31.
Castagnoli E., Mazzoleni P.,Generalized convexity for functions and multifunctions and optimality conditions, Report n.134, University of Pisa, 1986b.
Castagnoli E., Mazzoleni P.,Generalized connectedness for families of arcs. Optimization, 18(1), 1987, 3–16.
Castagnoli E., Mazzoleni P.,Scalar and vector generalized convexity, in [10],, 1989, 1–20.
Castagnoli E., Mazzoleni P.,Directional generalized convexity induced by differences, in [27], 1994a, 153–161.
Castagnoli E., Mazzoleni P.,Orderings, generalized convexity and monotonicity, in [23] Springer Verlag, 1994b, 250–262.
Clarke F. H., Dem'yanov V. F., Giannessi F., (eds.),Nonsmooth Optimization and Related Topics, Plenum Press, New York, 1989.
Dempe S., Pallaschke D.,Quasidifferentiability of optimal solutions in parametric nonlinear optimization, Optimization, 40, 1997, 1–24.
Dinklebach W.,On linear fractional programming, Management Science, 13, 1967, 492–498.
Fiacco A. V., Kyparisis J.,Convexity and concavity properties of the optimal value function in parametric nonlinear programming, J. of Optimization Theory and Applications, 48(1), 1986, 95–126.
Fiacco A. V., Kyparisis J.,Generalized convexity and concavity of the optimal value function in nonlinear programming, Mathematical Programming, 1987, 39, 195–304.
Furukawa N.,Parametric orders on fuzzy numbers and their roles in fuzzy optimization problems, Optimization, 40, 1997, 171–192.
Gal T.,Postoptimality Analysis, Parametric Programming, and Related Topics, 2nd Edition, Walter de Gruyter, Berlin, 1995.
Gal T., Greenberg H. J.,Advances in sensitivity analysis and parametric programming, Kluwer Acad. Publ., 1997.
Gauvin J.,Directional derivative for the value function in mathematical programming, in [10], 1989, 167–183.
Giorgi G.,Osservazioni sui teoremi di sensitività in programmazione matematica e in analisi economica, in Atti del Convegno AMASES, Genova, 9–12 settembre, 1998, 199–216.
Granot F., Veinott A. F. Jr.,Substitutes, complements and ripples in network flows, Mathematics of Operations Research, august, 10(3), 1985, 471–497.
Heller I.,Sensitivity analysis in linear programming, L.R.P. Seminar, Logistics Research Project (The George Washington University), 1954.
Kizbun A. I., Kan Y. S.,Stochastic Programming Problems with Probability and Quantile Functions, J. Wiley, 1995.
Komlósi S., Racpsák T., Schaible S., (eds.),Generalized Convexity, Springer Verlag, 1994.
Kuczma M.,An Introduction to the Theory of Functional Equations and Inequalities, Universytet Slaski, Varsavia, 1985.
Li Calzi M., Veinott Jr. A. F.,Lattice programming and subextremal functions, unpublished manuscript, july 1992.
Mazzoleni P.,Structural development of concavity properties, in [3], Springer Verlag, 1990, 14–22.
Mazzoleni P. (ed.),Optimization of generalized convex problems in economics, Stampa Bollo, Milano, 1994.
Mazzoleni P.,Proprietà di monotonia debole per problemi di ottimizzazione, inScritti in onore di G. Ottaviani, Edizioni Kappa, Roma, 1997a, 243–258.
Mazzoleni P.,Multiple projects for dynamic markets, Proceedings of the 1st International Workshop on Preferences and Decisions, Trento, june 5–7. University Press, Trento, 1997b, 73–76.
Mazzoleni P.,Generalized monotonicity for parametric problems, in Giorgi-Rossi (eds.)Convessità e Calcolo Parallelo, Libreria Universitaria Editrice, Verona, 1997c, 205–217.
Mazzoleni P.,Generalized monotonicity of the solution map, Atti del Convegno AMASES. Cosenza, 8–12 settembre 1999, 295–305.
Mukherjee R. N.,Arcwise connected functions and applications in multiobjective optimization, inOptimization, 39, 1997, 151–163.
Orchard, Hays W.,Notes on nonlinear programming (part 6): The RAND code for the simplex method. RAND Corporation Rep. n. 10, 1440, 1955.
Samuelson P. A.,Foundations of Economic Analysis, Anthenum, 1971 (Originally published by Harvard University Press, 1947).
Sawaragi Y., Nakayama H., Tanino T.,Theory of Multiobjective Optimization, Acad. Press, 1985.
Shimizu K., Ishizuka Y., Bard J. F.,Nondifferentiable and Two-level Mathematical Programming, Kluwer Acad., 1997.
Ward D. E.,Dini derivatives of the marginal function of a non-lipschitzian program, Siam J. of Optimization, 6(1), 1996, 198–211.
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Mazzoleni, P. Qualitative parametric optimization for applications. Decisions Econ Finan 22, 41–75 (1999). https://doi.org/10.1007/BF02912350
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DOI: https://doi.org/10.1007/BF02912350