First International Conference on Generalized Convexity Generalized Concavity in Optimization and Economics Vancouver (Canada), August 4-15, 1980

About 100 participants from 15 different countries attended the first international conference on Generalized Convexity held at the University of British Columbia, Vancouver, Canada, where over sixty lectures were given. This was a NATO Advanced Study Institute (ASI), which lasted two weeks. The proceedings constitute the first volume devoted to Generalized Convexity. This sizable book (767 pages) by Academic Press is now out of print (the first textbook on the subject appeared much later, but it was begun before this conference; see Avriel, M., Diewert,W.E., Schaible, S. and I. Zang, Generalized Concavity, Plenum Publishing Corporation, New York, 1988).

• AVRIEL Mordecai (Haifa, Israel)
• SCHAIBLE Siegfried (Edmonton, Alberta, Canada)
• ZIEMBA William T. (Vancouver, British Columbia, Canada)

• Schaible S. and W.T. Ziemba (Eds.), Generalized Concavity in Optimization and Economics, Proceedings of the “First Conference on Generalized Convexity”, held at University of British Columbia, Vancouver (British Columbia, Canada), August 4-15, 1980, Academic Press, New York, 1981.

1. Characterizations of generalized concave functions.
   • Avriel M., Diewert W.E., Schaible S. and W.T. Ziemba, Introduction to concave and generalized concave functions, pp.21-50.
   • Diewert W.E., Alternative characterizations of six kinds of quasiconcavity in the nondifferentiable case with applications to nonsmooth programming, pp.51-93.
   • Crouzeix J.P., Continuity and differentiability properties of quasiconvex functions on Rⁿ, pp.109-130.
   • Martin D.H., Connectedness of level sets as a generalization of concavity, pp.95-107.
   • Lindberg P.O., Power convex functions, pp.153-165.
   • Zang I., Concavifiability of C²-functions: a unified exposition, pp.131-152.
   
   
2. Generalized concave quadratic functions and C²-functions.
   • Crouzeix J.P. and J.A. Ferland, Criteria for quasiconvexity and pseudoconvexity and their relationships, pp.199-204.
   • Ferland J.A., Quasiconvexity and pseudoconvexity of functions on the nonnegative orthant, pp.169-181.
   • Schaible S., Generalized convexity of quadratic functions, pp.183-197.
   
   
3. Duality for generalized concave programs.
   • Crouzeix J.P., A duality framework in quasiconvex programming, pp.207-225.
   • Oettli W., Optimality conditions involving generalized convex mappings, pp.227-238.
   • Passy U., Pseudo duality and non-convex programming, pp.239-261.
   • Mond B. and T. Weir, Generalized concavity and duality, pp.263-279.
   • Di Guglielmo F., Estimates of the duality gap for discrete and quasiconvex optimization problems, pp.281-298.
   
   
4. New classes of generalized concave functions.
   • Borwein J.M., Convex relations in analysis and optimization, pp.335-377.
   • Ben-Tal A. and A. Ben-Israel, F-convex functions: properties and applications, pp.301-334.
   • Borwein J.M. and H. Wolkowicz, Cone-convex programming: stability and affine constraint functions, pp.379-397.
   • Brumelle S.L. and M.L. Puterman, Newton's method for w-convex operators, pp.399-414.
   
   
5. Fractional programming.
   • Craven B.D., Duality for generalized convex fractional programs, pp.473-489.
   • Cambini A., An algorithm for a special class of generalized convex programs, pp.491-508.
   • Ibaraki T., Solving mathematical programming problems with fractional objective functions, pp.441-472.
   • Schaible S., A survey of fractional programming, pp.417-440.
   
   
6. Applications of generalized concavity in management science and economics.
   • Diewert W.E., Generalized concavity and economics, pp.511-541.
   • Kannai Y., Concave utility functions-existence, constructions and cardinality, pp.543-611.
   • Weber R.J., Attainable sets of markets: an overview, pp.613-625.
   • Eichhorn W., Concavity and quasiconcavity in the theory of production, pp.627-636.
   • Eichhorn W. and W. Gehrig, Generalized convexity and the measurement of inequality, pp.637-642.
   • Von Hohenbalken B., The simplicial decomposition approach in optimization over polytopes, pp.643-659.
   • Jeroslow R., Some influences of generalized and ordinary convexity in disjunctive and integer programming, pp.689-699.
   • Craven B.D., Vector-valued optimization, pp.661-687.
   
   
7. Applications to stochastic systems.
   • Karlin S. and Y. Rinott, Univariate and multivariate total positivity, generalized convexity and related inequalities, pp.703-718.
   • Kallberg J.G. and W.T. Ziemba, Generalized concave functions in stochastic programming and portfolio theory, pp.719-767.