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TitleGeneralized Convexity and Fractional Programming with Economic Applications [electronic resource] : Proceedings of the International Workshop on "Generalized Concavity, Fractional Programming and Economic Applications" Held at the University of Pisa, Italy, May 30 - June 1, 1988 / edited by Alberto Cambini, Erio Castagnoli, Laura Martein, Piera Mazzoleni, Siegfried Schaible
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1990
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Descript VII, 361 p. online resource


Generalizations of convex functions have been used in a variety of fields such as economics. business administration. engineering. statistics and applied sciences.ยท In 1949 de Finetti introduced one of the fundamental of generalized convex functions characterized by convex level sets which are now known as quasiconvex functions. Since then numerous types of generalized convex functions have been defined in accordance with the need of particular applications.ยท In each case such functions preserve soine of the valuable properties of a convex function. In addition to generalized convex functions this volume deals with fractional programs. These are constrained optimization problems which in the objective function involve one or several ratios. Such functions are often generalized convex. Fractional programs arise in management science. economics and numerical mathematics for example. In order to promote the circulation and development of research in this field. an international workshop on "Generalized Concavity. Fractional Programming and Economic Applications" was held at the University of Pisa. Italy. May 30 - June 1. 1988. Following conferences on similar topics in Vancouver. Canada in 1980 and in Canton. USA in 1986. it was the first such conference organized in Europe. It brought together 70 scientists from 11 countries. Organizers were Professor A. Cambini. University of Pisa. Professor E. Castagnoli. Bocconi University. Milano. Professor L. Martein. University of Pisa. Professor P. Mazzoleni. University of Verona and Professor S. Schaible. University of California. Riverside


I. Generalized Convexity -- to generalized convexity -- Structural developments of concavity properties -- Projectively-convex models in economics -- Convex directional derivatives in optimization -- Differentiable (? , ?)-concave functions -- On the bicriteria maximization problem -- II. Fractional Programming -- Fractional programming โ{128}{148} some recent results -- Recent results in disjunctive linear fractional programming -- An interval-type algorithm for generalized fractional programming -- A modified Kelleyโ{128}{153}s cutting plane algorithm for some special nonconvex problems -- Equivalence and parametric analysis in linear fractional programming -- Linear fractional and bicriteria linear fractional programs -- III. Duality and Conjugation -- Generalized conjugation and related topics -- On strongly convex and paraconvex dualities -- Generalized convexity and fractional optimization -- Duality in multiobjective fractional programming -- An approach to Lagrangian duality in vector optimization -- Rubinstein Duality Scheme for Vector Optimization -- IV. Applications of Generalized Convexity in Management Science and Economics -- Generalized convexity in economics: some examples -- Log-Convexity and Global Portfolio Immunization -- Improved analysis of the generalized convexity of a function in portfolio theory -- On some fractional programming models occurring in minimum-risk problems -- Quasi convex lower level problem and applications in two level optimization -- Problems of convex analysis in economic dynamical models -- Recent bounds in coding using programming techniques -- Logical aspects concerning Shephardโ{128}{153}s axioms of production theory -- Contributing Authors

Mathematics Operations research Decision making Applied mathematics Engineering mathematics System theory Calculus of variations Economic theory Mathematics Applications of Mathematics Operation Research/Decision Theory Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory Control Calculus of Variations and Optimal Control; Optimization


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