Generalized Convexity

1. Front Matter

   Pages i-viii

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2. Generalized Convex Functions

   1. Front Matter

      Pages 1-1

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   2. Univex sets, functions and univex nonlinear programming

      • C. R. Bector, S. Chandra, S. Gupta, S. K. Suneja

      Pages 3-18

   3. Optimization on closely convex sets

      • Lucia Blaga, József Kolumbán

      Pages 19-34

   4. A note on ordinal concavity

      • Margherita Cigola

      Pages 35-39

   5. Generalized concavity in cooperative game theory: characterizations in terms of the core

      • Theo Driessen

      Pages 40-52

   6. On the existence of Nash-equilibrium in n-person generalized concave games

      • Ferenc Forgó

      Pages 53-61

   7. A deep cut ellipsoid algorithm and quasiconvex programming

      • J. G. B. Frenk, J. Gromicho, F. Plastria, S. Zhang

      Pages 62-76

   8. Quasiconvexity and related properties in the calculus of variations

      • H. Hartwig

      Pages 77-84

   9. Ray-quasiconvex and f-quasiconvex functions

      • J. A. Mayor-Gallego, A. Rufián-Lizana, P. Ruiz-Canales

      Pages 85-90

   10. Geodesic convexity on ℝ ⁿ

       • T. Rapcsák

       Pages 91-103

   11. A class of differentiable generalized convex functions

       • P. Szilágyi

       Pages 104-115

   12. Equivalence between generalized gradients and subdifferentials for a suitable class of lower semicontinuos functions

       • Mario Tosques

       Pages 116-133

3. Optimality and Duality

   1. Front Matter

      Pages 135-135

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   2. Generalizing convexity for second order optimality conditions

      • Gabriele Danninger, Immanuel M. Bomze

      Pages 137-144

   3. Regularity conditions for constrained extremum problems via image space approach: the linear case

      • P. H. Dien, G. Mastroeni, M. Pappalardo, P. H. Quang

      Pages 145-152

   4. Duality theory for convex/quasiconvex functions and its application to optimization

      • J. G. B. Frenk, D. M. L. Dias, J. Gromicho

      Pages 153-170

   5. First order generalized optimality conditions for programming problems with a set constraint

      • G. Giorgi, A. Guerraggio

      Pages 171-185

   6. Abstract nonsmooth nonconvex programming

      • B. M. Glover, V. Jeyakumar

      Pages 186-210

   7. A survey on optimality and duality in nonsmooth programming

      • Stefan Mititelu

      Pages 211-225

Generalizations of the classical concept of a convex function have been proposed in various fields such as economics, management science, engineering, statistics and applied sciences during the second half of this century. In addition to new results in more established areas of generalized convexity, this book presents several important developments in recently emerging areas. Also, a number of interesting applications are reported.

• Convexity
• Generalized convex functions
• Quotientenprogrammierung
• Scheduling
• Verallgemeinerte konvexe Funktionen
• Verallgemeinerte monotone Abbildungen
• algorithms
• fractional programming
• game theory
• generalized monotone maps
• linear optimization
• nonlinear optimization
• optimization

• Faculty of Economics, Janus Pannonius University, Pécs, Hungary

  Sándor Komlósi

• Computer and Automation Institute, Hungary Academy of Sciences, Budapest, Hungary

  Tamás Rapcsák

• Graduate School of Management, University of California, Riverside, USA

  Siegfried Schaible

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