Who We Are - WGGC Activities

• The Working Group on Generalized Convexity (WGGC) was founded during the 15th International Symposium on Mathematical Programming in Ann Arbor (Michigan, U.S.A.), August 1994. It is a growing, interdisciplinary group of scholars from operations research, economics, engineering, applied sciences, mathematics, statistics, among others, with an interest in generalizations of the classical concept of a convex function. Models involving such functions have a significantly wider range of applicability than convex models.
   
• Much of the earlier work in generalized convexity was done by researchers in mathematical programming (e.g., Avriel, Fenchel, Mangasarian, Martos) and in economic theory (e.g., Arrow, Diewert, Eichhorn, Kannai). To this day, both disciplines continue to benefit from this kind of research. In addition, generalized convexity has been studied in management science, engineering, applied sciences, mathematics, statistics, for example. We also mention fractional programming (optimization of ratios of functions) with well over onethousand publications which significantly overlaps with generalized convexity. On the other hand, a nontraditional topic such as abstract convexity is gaining interest now too.
  Another recent development in generalized convexity has been the study of generalized monotone maps, introduced in such a way that in case of gradientmaps generalized monotonicity characterizes generalized convexity of the underlying function. Generalized monotone maps play a role in complementarity problems, variational inequalities and, more generally, equilibrium problems arising in various disciplines.
   
• Like in other areas of mathematical programming, contributions in generalized convexity/monotonicity range from theoretical and algorithmic to computational and applied research.
   
• The activities of WGGC are guided by the International Scientific Committee and its Chair (Prof. Siegfried Schaible 1994-1997, Prof. Sándor Komlósi 1997-2000, Prof. Juan-Enrique Martinez-Legaz 2000-2002, Prof. Siegfried Schaible 2002-2003, Prof. Nicolas Hadjisavvas 2003-2006, Prof. Siegfried Schaible 2006-2009).
   
• WGGC holds clusters of invited sessions at the international symposia on mathematical programming (Ann Arbor 1994, Lausanne 1997, Atlanta 2000, Copenhagen 2003). In addition, it is regularly represented through sessions at other major international conferences (see the Conferences Area).
   
• Furthermore, WGGC organizes international symposia as well as regional workshops and conferences. The international symposia will take place at three-year intervals from now on. Previous international symposia on generalized convexity were held in Vancouver/Canada (NATO - ASI) in 1980, Canton/U.S.A. in 1986, Pisa/Italy in 1988, Pécs/Hungary in 1992, Marseille/France in 1996, Samos/Greece in 1999, Hanoi/Vietnam in 2002 and Varese/Italy in 2005.
   
• Announcements and reports of the triennal international symposia have regularly appeared in Optima, the newsletter of the Mathematical Programming Society. Like in the past, ties to neighboring fields were strengthened through tutorials by R.E. Burkard (combinatorial optimization), B. Mordukhovich (nonsmooth analysis) and H. Tuy (global optimization) at the 7th International Conference on Generalized Convexity.
   
• The proceedings of the international symposia were published by Academic Press (1981), Analytic Publishing (1989), Springer Verlag (1990, 1994, 2001,2005) and Kluwer Academic Publishers (1998). In addition, proceedings of some of the regional workshops are available. See the Proceedings Area.
   
• Apart from books on special topics, a monograph on generalized convexity was published by Plenum Publishing Corporation in 1988, authored by Avriel, Diewert, Schaible and Zang. The Handbook of Generalized Convexity and Generalized Monotonicity was also published by Springer in 2005, authored by Hadjisavvas, Komlósi and Schaible. See the GCM books Area.
   
• The "Working Group on Generalized Convexity" has 427 members from 50 countries.