Almost Convex Functions: Conjugacy and Duality

1. Aleman A (1985) On some generalizations of convex sets and convex functions. Mathematica-Revue d’Analyse Numérique et de la Théorie de l’Approximation 14:1–6

   MATH  MathSciNet  Google Scholar 

2. Blaga L, Kolumbán J (1994) Optimization on closely convex sets. In: Generalized Convexity (Pécs, 1992), Lecture Notes in Economics and Mathematical Systems 405. Springer, Berlin, pp. 19–34

   Google Scholar 

3. Botţ RI, Grad SM, Wanka G (2005) Fenchel’s duality theorem for nearly convex functions. Preprint 13/2005, Faculty of Mathematics, Chemnitz University of Technology

   Google Scholar 

4. Botţ RI, Kassay G, Wanka G (2005) Strong duality for generalized convex optimization problems. Journal of Optimization Theory and Applications 127(1):45–70

   Article  MathSciNet  Google Scholar 

5. Botţ RI, Wanka G (2006) A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. Nonlinear Analysis: Theory, Methods & Applications 64(12):2787–2804

   Article  MathSciNet  Google Scholar 

6. Breckner WW, Kassay G (1997) A systematization of convexity concepts for sets and functions. Journal of Convex Analysis 4(1):109–127

   MATH  MathSciNet  Google Scholar 

7. Cobzaaş Ş, Muntean I (1987) Duality relations and characterizations of best approximation for p-convex sets. L’Analyse Numérique et la Théorie de l’Approximation 16(2):95–108

   Google Scholar 

8. Frenk JBG, Kassay G (2005) Introduction to convex and quasiconvex analysis. In: Handbook of Generalized Convexity and Generalized Monotonicity, Nonconvex Optimization and its Applications 76. Springer, New York, pp. 3–87

   Chapter  Google Scholar 

9. Frenk JBG, Kassay G, Lagrangian duality and convexlike functions. Journal of Optimization Theory and Applications (to appear)

   Google Scholar 

10. Frenk JBG, Kassay G (2002) Minimax results and finite-dimensional separation. Journal of Optimization Theory and Applications 113(2):409–421

    Article  MATH  MathSciNet  Google Scholar 

11. Hamel G (1905) Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: f(x + y) = f(x) + f(y). Mathematische Annalen 60:459–462

    Article  MATH  MathSciNet  Google Scholar 

12. Jeyakumar V, Gwinner J (1991) Inequality systems and optimization. Journal of Mathematical Analysis and Applications 159(1):51–71

    Article  MATH  MathSciNet  Google Scholar 

13. Kolumbán J, Blaga L (1990) On the weakly convex sets. Studia Universitatis Babeaş-Bolyai Mathematica 35(4):13–20

    MATH  Google Scholar 

14. Muntean I (1985) Support points of p-convex sets. In: Proceedings of the Colloquium on Approximation and Optimization (Cluj-Napoca, 1985). University of Cluj-Napoca, Cluj-Napoca, pp. 293–302

    Google Scholar 

15. Paeck S (1992) Convexlike and concavelike conditions in alternative, minimax, and minimization theorems. Journal of Optimization Theory and Applications 74(2):317–332

    Article  MATH  MathSciNet  Google Scholar 

16. Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton

    MATH  Google Scholar 

17. Sach PH (2005) New generalized convexity notion for set-valued maps and application to vector optimization. Journal of Optimization Theory and Applications 125(1):157–179

    Article  MATH  MathSciNet  Google Scholar 

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