Conjugacy in quasi-convex programming

1. J.P. Crouzeix, “Contributions a l'étude des functions quasiconvex”, Thesis, Université de Clermont II (France, 1977).

   Google Scholar 

2. J.P. Crouzeix, “A duality framework in quasi convex programming”, in: S. Schaible and W.T. Ziemba, eds.,Generalized concavity in optimization and economics (Academic Press, New York, 1981) pp. 207–225.

   Google Scholar 

3. J.P. Crouzeix, “Continuity and differentiability properties of quasiconvex functions on ℝ”, in: S. Schaible and W.T. Ziemba, eds.,Generalized concavity in optimization and economics (Academic Press, New York, 1981) pp. 109–130.

   Google Scholar 

4. W. Fenchel, “Convex cones, sets and functions”, Lecture Notes, Princeton University (Princeton, NJ, 1951).

   Google Scholar 

5. W. Fenchel, “A remark on convex sets and polarity”, Communication Seminar on Mathematics, University of Lung Supplementary Volume (University of Lund, Lund, 1952) 22–89.

6. J. Flachs and M.A. Pollatschek, “Duality theorems for certain programs involving minimum or maximum operations,”Mathematical Programming 16 (1979) 348–370.

   Article  MATH  MathSciNet  Google Scholar 

7. H.J. Greenberg and W.P. Pierskalla, “Quasi-conjugate functions and surrogate duality”,Cahiers due Center d'Etudes de Recherche Opérationnelle 15 (1973) 437–448.

   MATH  MathSciNet  Google Scholar 

8. V.L. Klee, “Maximal separation theorem for convex sets”,Transactions of the American Mathematical Society 134 (1968) 133–148.

   Article  MATH  MathSciNet  Google Scholar 

9. J.E. Martinez Legaz, “Exact quasiconvex conjugation”, Departmento de Educaciones Functionales. Universidad de Barcelona, Spain, presented at the 11th International Symposium on Mathematical Programming (Bonn, 1982).

10. W. Oettli, “Optimality conditions involving generalized convex mappings”, in: S. Schaible and W.T. Ziemba, eds.,Generalized concavity in optimization and economics (Academic Press, New York, 1981) pp. 227–238.

    Google Scholar 

11. E.Z. Prisman, “A new approach to duality Lagrangians and saddle functions in quasi convex programming”, Ph.D. Dissertation, Technion (Haifa, Israel, 1982) (in Hebrew).

    Google Scholar 

12. R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).

    MATH  Google Scholar 

13. I. Singer, “Pseudo-conjugate functionals and pseudo-duality”, in: Proceedings of the International Conference in Mathematical Methods in Operations Research Sofia (Publishing House of the Bulgarian Academy of Science, Sofia, 1980).

    Google Scholar 

14. Y.I. Zabotin, A.I. Korablev and R.F. Khabibullin, “Conditions for an extremum of a functional in case of constraints”,Cybernetics 9 (1975) 982–988.

    Article  Google Scholar 

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