A Summer School preceded the Symposium being held from August 25 to August 28, 1999, at the same place as the Symposium (Karlovassi, Samos, Greece). The Summer School aimed to introduce graduate and PhD students, as well as scientists from other fields, to the subject of Generalized Convexity and Generalized Monotonicity.

Program of the School

• Introduction to convexity and generalized convexity (J.B.G. Frenk) – Course notes
• Continuity and differentiability of generalized convex functions (J.P. Crouzeix) – Course notes
• 1st and 2nd order characterizations of Generalized Convexity (J.P. Crouzeix) – Course notes
• Generalized convexity and nonsmooth analysis (J.P. Penot) – Course notes
• Generalized monotone single valued maps (S. Schaible) (**)
• Generalized monotone multi valued maps – Generalized monotonicity in variational inequalities (N. Hadjisavvas)(**)
• Generalized monotonicity in equilibrium problems (S. Schaible)(**)
• Duality and application to economics (J.E. Martinez-Legaz) (*)
• Uses of generalized convexity in economics (J.E. Martinez-Legaz) (*)
• Fractional programming (S. Schaible)(**)
• Vector optimization (D.T. Luc) – Course notes
• Introduction to global optimization and its applications (P. Pardalos) – Course notes

(*) See the following papers:
– Martinez-Legaz J.-E., “Duality between direct and indirect utility functions under minimal hypotheses”, Journal of Mathematical Economics, vol.20, pp.199-209, 1991.
– Martinez-Legaz J.-E. and M.S. Santos, “Duality between direct and indirect preferences”, Economic Theory, vol.3, pp.335-351, 1993.
– Martinez-Legaz J.-E. and M.S. Santos, “On expenditure functions”, Journal of Mathematical Economics, vol.25, pp.143-163, 1996.
– Martinez-Legaz J.-E., “Quasiconvex duality theory by generalized conjugatio methods”, Optimization, vol.19, no.5, pp.603-652, 1988.

(**) Notes to appear in “Encyclopedia of Optimization”, edited by Floudas C. and P. Pardalos, Kluwer Academic Publishers, Dordrecht.