By S. Schaible (auth.), Prof. Dr. Alberto Cambini, Prof. Dr. Erio Castagnoli, Prof. Dr. Laura Martein, Prof. Dr. Piera Mazzoleni, Prof. Dr. Siegfried Schaible (eds.)

ISBN-10: 3540526730

ISBN-13: 9783540526735

ISBN-10: 3642467091

ISBN-13: 9783642467097

Generalizations of convex features were utilized in various fields corresponding to economics. company management. engineering. records and utilized sciences.· In 1949 de Finetti brought one of many basic of generalized convex services characterised by means of convex point units that are referred to now as quasiconvex services. in view that then a variety of different types of generalized convex features were outlined in keeping with the necessity of specific applications.· In every one case such capabilities shield soine of the dear homes of a convex functionality. as well as generalized convex capabilities this quantity bargains with fractional courses. those are restricted optimization difficulties which within the target functionality contain one or numerous ratios. Such features are frequently generalized convex. Fractional courses come up in administration technological know-how. economics and numerical arithmetic for instance. so that it will advertise the circulate and improvement of analysis during this box. a global workshop on "Generalized Concavity. Fractional Programming and monetary purposes" was once held on the college of Pisa. Italy. could 30 - June 1. 1988. Following meetings on comparable issues in Vancouver. Canada in 1980 and in Canton. united states in 1986. it used to be the 1st such convention prepared in Europe. It introduced jointly 70 scientists from eleven international locations. Organizers have been Professor A. Cambini. college of Pisa. Professor E. Castagnoli. Bocconi collage. Milano. Professor L. Martein. collage of Pisa. Professor P. Mazzoleni. collage of Verona and Professor S. Schaible. college of California. Riverside.

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Extra info for Generalized Convexity and Fractional Programming with Economic Applications: Proceedings of the International Workshop on “Generalized Concavity, Fractional Programming and Economic Applications” Held at the University of Pisa, Italy, May 30 – June 1, 198

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If f is directionally Lipschitzian at x, there exist y E E and Y E N(y) such that [O(x; 0) is bounded above on Y (see (20)). , (18)) implies that fL 00 (x; 0) (fU oo (x; 0)) is bounded above and> -00 on Y. Therefore assertion (a) is valid. 5 for B: = L, D: = U. 8. c. for each i E I(x o), and that (21) dom fLoo(X o: 0) () () int dom giUoo(Xo: 0) .. ~. I(xo) Then for each h E GUC(L, f, xo) and hi E GUC(U, gi' xo)' there exist Ai least one of which is nonzero, such that o E Aoi>h(O) + (22) (23) domfLOO(xO:o) () L 2 0, i E I(x o) U (O), at Aii>hi(O) 1(10) () (YlgiUOO(10:Y)<0)"~' 1(10 ) then Ao> 0 in (22).

If T is assumed to be P-convex. x)). x). Assuming that T is P-convex is less restrictive than the common approach of assuming that T is convex (see. for example. Banker et a1. (1984)). 4. paration Theorem An interesting theoretical and practical question is whether or not one would ever observe the "P-convex portion" of the technology. , those boundary points of the level set lying in the interior of the convex hull of the level set (points A. Band C in Figure 4). If the production planner were cost minimizing (one possible behavioral assumption), then points A.

A useful generalization of convexity must fulfill two requirements. First. and foremost, it must admit a rich class of economic models. Second. it must be tractable for analysis. e .. it 24 must have some useful mathematical structure. Recently, Hackman and Passy (1988) introduced a generalization of convexity called Projective-convexity or (P-convexity) according to the second approach. It was shown that P-convexity has the requisite mathematical structure. For example, P-convex sets possess a separation property (as in the first approach to generalizing convexity): a point not in a closed P-convex set can be separated by a quadrant, which is an intersection of closed halfspaces generated by orthogonal hyperplanes.

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Generalized Convexity and Fractional Programming with Economic Applications: Proceedings of the International Workshop on “Generalized Concavity, Fractional Programming and Economic Applications” Held at the University of Pisa, Italy, May 30 – June 1, 198 by S. Schaible (auth.), Prof. Dr. Alberto Cambini, Prof. Dr. Erio Castagnoli, Prof. Dr. Laura Martein, Prof. Dr. Piera Mazzoleni, Prof. Dr. Siegfried Schaible (eds.)


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