**Karlovassi-Samos (Greece)****August 30 – September 3, 1999**

The 6th International Symposium on Generalized Convexity and Monotonicity was held at the Department of Mathematics of the University of the Aegean in Karlovassi-Samos (Greece), from August 30 to September 3, 1999. About 100 participants from 22 different countries attended the conference and over sixty lectures were given.

The Symposium and its preceding Summer School were organized by the Working Group on Generalized Convexity (WGGC). Topics covered included various kinds of generalized convex functions and generalized monotone maps, optimality conditions, duality, fractional programming, multi-objective programming, nonsmooth analysis, variational inequalities, equilibrium problems as well as topics less represented at previous symposia such as stochastic convexity and global optimization. Furthermore, as at the last symposium, several invited lectures introduced participants to neighboring fields of generalized convexity. This time set-valued optimization, multiplicative/fractional programming, global optimization and stochastic programming were the emphasis with tutorials by J.Jahn (Germany), H.Konno (Japan), P.M.Pardalos (USA) and A.Prekopa (USA), respectively. The Symposium was hosted by the Department of Mathematics of the University of the Aegean, located on Samos, the birthplace of Pythagoras and Aristarchus. This truly scenic island with its interesting archeological sites gave the conference a special background.

The website of the Summer School and the Symposium was available at http://www.samos.aegean.gr/math/gc6/.

Details on the **conference proceedings** are available at this link.

**Available Documents**

- HADJISAVVAS Nicolas (Samos, Greece) (Chair)
- CAMBINI Riccardo (Pisa, Italy)
- DANIILIDIS Aris (Pau, France)
- FRENK J.B.J. (Rotterdam, The Netherlands)
- SCHAIBLE Siegfried (Riverside, California, U.S.A.)

“Generalized Convexity and Generalized Monotonicity”, edited by N. Hadjisavvas, J.E. Martinez-Legaz and J-P. Penot, Lecture Notes in Economics and Mathematical Systems, vol.502, 410 pp., ISBN 3-540-41806-7, Springer-Verlag, 2001.

Details on the book are available at this page.

These are the invited papers for the Conference Proceedings :

- Konno H., Minimization of the sum of several linear fractional functions, pp.3-20.
- Prékopa A., Discrete higher order convex functions and their applications, pp.21-47.
- Yajima Y., Ramana M.V. and P.M. Pardalos, Cuts and semidefinite relaxations for nonconvex quadratic problems, pp.48-70.

These are the contributed papers selected for the Conference Proceedings :

- Albrecht J. and D. Cieslik, The Steiner ratio of Lp3, pp.73-87.
- Aussel D. and A. Daniilidis, Normal cones to sublevel sets: an axiomatic approach. Applications in quasiconvexity and pseudoconvexity, pp.88-101.
- Beato-Moreno A., Osuna-Gómez R., Rufián-Lizana A. and P. Ruiz-Canales, Multiobjective programming with rho-convex functions, pp.102-116.
- Bhatia D. and P. Kumar, Vector invex n-set functions and minmax programming, pp.117-128.
- Cambini A., Carosi L. and L. Martein, On the supremum in quadratic fractional programming, pp.129-143.
- Cambini R. and L. Martein, First and second order characterizations of a class of pseudoconcave vector functions, pp.144-158.
- Caristi G., Ferrara M. and A. Stefanescu, New invexity-type conditions in constrained optimization, pp.159-166.
- Denuit M. and C. Lefèvre, Stochastic s-(increasing) convexity, pp.167-182.
- Djafari-Rouhani B., Tarafdar E. and P.J. Watson, Fixed points theorems, coincidence theorems and variational inequalities, pp.183-188.
- Ferrer Biosca A., Representation of a polynomial function as a difference of convex polynomials, with an application, pp.189-207.
- Giorgi G. and A. Guerraggio, Proper efficiency and generalized convexity in nonsmooth vector optimization problems, pp.208-217.
- Gupta P. and D. Bathia, Duality for fractional min-max problems involving arcwise connected and generalized arcwise connected functions, pp.218-230.
- Hansen G.L. and J.C. Dupin, Generalized convexity for unbounded sets: the enlarged space, pp.231-239.
- John R., A note on Minty variational inequalities and generalized monotonicity, pp.240-246.
- Konnov I.V., On vector equilibrium and vector variational inequality problems, pp.247-263.
- Müller A., Stochastic orders generated by generalized convex functions, pp.264-278.
- Páles Z., Separation theorems for convex sets and convex functions with invariance properties, pp.279-293.
- Penot J.P. and M. Volle, Convexity and generalized convexity methods for the study of Hamilton-Jacobi equations, pp.294-316.
- Pestana D.D. and S. Mendonça, Higher-order monotone functions and probability theory, pp.317-331.
- Petrusel A. and G. Mot, Convexity and decomposability in multivalued analysis, pp.332-340.
- Popovici N., Scalar characterization of generalized quasiconvex functions, pp.341-348.
- Preda V. and I.M. Stancu-Minasian, Optimality and Wolfe duality for multiobjective programming problems involving n-set functions, pp.349-361.
- Redaelli G., Vector stochastic optimization problems, pp.362-380.
- Singer I., On suprema of abstract convex and quasi-convex hulls, pp.381-394.
- Tigan S., Stancu-Minasian I.M. and I. Tigan, Specific numerical methods for solving some special max-min programming problems involving generalized convex functions, pp.395-410.