Summer School on Generalized Convexity

Karlovassi-Samos (Greece),
August 25 - 28, 1999

 

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.

Thanks to the efforts of M.Sniedovich, IFORS representative, the three best students of the Summer School obtained an IFORS scholarship.

Director of the Summer School: J.B.G. Frenk

Program of the School

  • Introduction to convexity and generalized convexity (J.B.G. Frenk) Notes Available in .pdf and .ps formats.
  • Continuity and differentiability of generalized convex functions (J.P. Crouzeix) Notes Available in .pdf and .dvi formats.
  • 1st and 2nd order characterizations of Generalized Convexity (J.P. Crouzeix) Notes Available in .pdf formats.
  • Generalized convexity and nonsmooth analysis (J.P. Penot) Notes Available in .pdf and .dvi formats.
  • 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) Notes Available in .pdf and .ps formats.
  • Introduction to global optimization and its applications (P. Pardalos) Notes Available in .pdf and .ps formats.
(*) 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.

 

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