Generalized Convexity and Fractional Programming with Economic Applications

This proceedings volume brings together latest research results on generalized convexity and fractional programming from mathematics, economics, operations research and management science. The state of the art in the field is presented.

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This volume contains invited articles and refereed contributions presented at an international workshop held at the University of Pisa in 1988. The subject of the book is generalizations of the classical concept of a convex function. Many of these generalizations are prompted by applications in economics. In addition, special types of generalized convex programs, namely fractional programs, are presented. The book is interdisciplinary, and brings together the most recent developments in these fields from mathematics, economics, operations research and management science. It presents the state of the art in the fields of generalized convexity and fractional programming.

Contenu
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 some recent results.- Recent results in disjunctive linear fractional programming.- An interval-type algorithm for generalized fractional programming.- A modified Kelley'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 Shephard's axioms of production theory.- Contributing Authors.