Fifth International Conference on Generalized Convexity Convexité Généralisée Luminy-Marseille (France), June 17-21, 1996

About 70 participants from 13 different countries attended the fifth international conference on Generalized Convexity held at the Centre International de Rencontres Mathématiques (CIRM), Luminy-Marseille (France), where over 50 talks were given. This was the first International Symposium on Generalized Convexity which was organized by the Working Group on Generalized Convexity, founded in 1994. It was also the first symposium in the series which was sponsored by the Mathematical Programming Society. Furthermore, the Mathematical Research Center of France CIRM lent its support to this important event in applied mathematics. In contrast to previous symposia, GCV had a stronger emphasis on generalized monotonicity. Another novelty at GCV, well received by the participants, was the inclusion of three invited lectures from scholars of neighboring fields, namely nonsmooth analysis (F.Clarke), mathematical programming/complementarity problems/variational inequalities (J.S.Pang) and stochastic programming (R.Wets). The proceedings of the conference have been published in a 480 page volume by Kluwer Academic Publishers.

• AUSSEL Didier (Perpignon, France)
• CROUZEIX Jean-Pierre (Clermont-Ferrand, France) (chair)
• MARTINEZ-LEGAZ Juan-Enrique (Barcelona, Spain)
• SCHAIBLE Siegfried (Riverside, California, U.S.A.)
• SEEGER Alberto (Avignon, France)
• VOLLE Michel (Avignon, France)

• Crouzeix J.P., Martinez-Legaz J.E. and M. Volle (Eds.), Generalized Convexity, Generalized Monotonicity, Proceedings of the “Fifth International Symposium on Generalized Convexity”, held at the Centre International de Rencontres Mathématiques (CIRM), Luminy-Marseille (France), June 17-21, 1996, Nonconvex Optimization and Its Applications, vol.27, Kluwer Academic Publishers, Dordrecht, 1998.

1. Generalized Convexity.
   • Penot J.P., Are generalized derivatives useful for generalized convex functions?, pp.3-60.
   • Wets R.J.B., Stochastic programs with chance constraints: generalized convexity and approximation issues, pp.61-74.
   • Lewis A.S. and J.S. Pang, Error bounds for convex inequality systems, pp.75-110.
   • Eberhard A., Nyblom M. and D. Ralph, Applying generalised convexity notions to Jets, pp.111-158.
   • Rubinov A.M. and B.M. Glover, Quasiconvexity via two step functions, pp.159-184.
   • Jourani A. and M. Théra, On limiting Fréchet epsilon-subdifferentials, pp.185-198.
   • Blaga L. and L. Lupsa, Convexity space with respect to a given set, pp.199-208.
   • Precupanu A.M., A convexity condition for the nonexistence of some antiproximinal sets in the space of integrable functions, pp.209-218.
   • Castellani M. and M. Pappalardo, Characterizations of rho-convex functions, pp.219-234.
   
   
2. Generalized Monotonicity.
   • Crouzeix J.P., Characterizations of generalized convexity and generalized monotonicity, a survey, pp.237-256.
   • Hadjisavvas N. and S. Schaible, Quasimonotonicity and pseudomonotonicity in variational inequalities and equilibrium problems, pp.257-276.
   • Cambini R. and S. Komlósi, On the scalarization of pseudoconcavity and pseudomonotonicity concepts for vector valued functions, pp.277-290.
   • John R., Variational inequalities and pseudomonotone functions: some characterizations, pp.291-302.
   
   
3. Optimality Conditions and Duality.
   • Flores-Bazán F. and J.E. Martinez-Legaz, Simplified global optimality conditions in generalized conjugation theory, pp.305-330.
   • Lemaire B. and M. Volle, Duality in DC programming, pp.331-346.
   • Cambini A., Komlósi S. and L. Martein, Recent developments in second order necessary optimality conditions, pp.347-356.
   • Mond B. and J. Zhang, Higher order invexity and duality in mathematical programming, pp.357-372.
   • Bector C.R., Chandra S. and V. Kumar, Fenchel duality in generalized fractional programming, pp.373-386.
   
   
4. Vector Optimization.
   • Giorgi G. and A. Guerraggio, The notion of invexity in vector optimization: smooth and nonsmooth case, pp.389-406.
   • Molho E. and A. Zaffaroni, Quasiconcavity of sets and connectedness of the efficient frontier in ordered vector spaces, pp.407-424.
   • Beato-Moreno A., Ruiz-Canales P., Luque-Calvo P.L. and R. Blanquero-Bravo, Multiobjective quadratic problem: characterization of the efficient points, pp.425-438.
   • R. Cambini, Generalized concavity for bicriteria functions, pp.439-452.
   • Cambini A. and L. Martein, Generalized concavity in multiobjective programming, pp.453-468.