Duality for quasiconvex minimization over closed convex cones

1. Balder, E.J.: An extension of duality-stability relations to nonconvex optimization problems. SIAM J. Control Optim. 15(2), 329–343 (1977)

   Article  MathSciNet  Google Scholar 

2. Crouzeix, J.-P.: Polaires quasi-convexes et dualité. (French). C. R. Acad. Sci. Paris Sér. A 279, 955–958 (1974)

   MathSciNet  MATH  Google Scholar 

3. Crouzeix, J.-P.: Conjugacy in quasiconvex analysis. Convex analysis and its applications (Proc. Conf., Muret-le-Quaire, 1976), pp. 66–99

4. Crouzeix, J.-P.: Contributions à l’étude des fonctions quasiconvexes. (French) Thèse présentée à l’Université de Clermont-Ferrand II (U.E.R. des Sciences Exactes et Naturelles à dominante Recherche) pour obtenir le grade de Docteur ès Sciences Math ématiques. Série: E, No. d’Ordre 250. Université de Clermont-Ferrand II, Clermont-Ferrand, (1977)

5. Dolecki, S., Kurcyusz, S.: On \(\Phi \)-convexity in extremal problems. SIAM J. Control Optim. 16(2), 277–300 (1978)

   Article  MathSciNet  Google Scholar 

6. Fajardo, M.D., Goberna, M.A., Rodríguez, M.M.L., Vicente-Pérez, J.: Even Convexity and Optimization. Handling Strict Inequalities. EURO Advanced Tutorials on Operational Research. Springer, Cham (2020)

   MATH  Google Scholar 

7. Greenberg, H.-J., Pierskalla, W.P.: Surrogate mathematical programming. Op. Res. 18, 924–939 (1970)

   Article  MathSciNet  Google Scholar 

8. Greenberg, H.J., Pierskalla, W.P.: Quasi-conjugate functions and surrogate duality. Cahiers Centre Études Rech. Opér. 15, 437–448 (1973)

   MathSciNet  MATH  Google Scholar 

9. Kilp, M., Knauer, U., Mikhalev, A. V.: Monoids, acts and categories. With applications to wreath products and graphs. A handbook for students and researchers. de Gruyter Expositions in Mathematics. 29. Walter de Gruyter, Berlin, (2000)

10. Lindberg, P. O.: A generalization of Fenchel conjugation giving generalized Lagrangians and symmetric nonconvex duality. Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 1, pp. 249–267, North-Holland, Amsterdam-Oxford-New York, (1979)

11. Luenberger, D.G.: Quasi-convex programming. SIAM J. Appl. Math. 16, 1090–1095 (1968)

    Article  MathSciNet  Google Scholar 

12. Martínez-Legaz, J. E.: A generalized concept of conjugation. Optimization: theory and algorithms (Confolant, 1981), 45–59, Lecture Notes in Pure and Appl. Math., 86, Dekker, New York, (1983)

13. Martínez-Legaz, J. E.: A new approach to symmetric quasiconvex conjugacy. Selected topics in operations research and mathematical economics (Karlsruhe, 1983), 42–48, Lecture Notes in Econom. and Math. Systems, 226, Springer, Berlin, (1984)

14. Martínez-Legaz, J.E.: Quasiconvex duality theory by generalized conjugation methods. Optimization 19(5), 603–652 (1988)

    Article  MathSciNet  Google Scholar 

15. Martínez-Legaz, J. E.: On lower subdifferentiable functions. Trends in mathematical optimization (Irsee, 1986), 197–232, Internat. Schriftenreihe Numer. Math., 84, Birkhäuser, Basel, (1988)

16. Martínez-Legaz, J. E.: Fenchel duality and related properties in generalized conjugation theory. International Conference in Applied Analysis (Hanoi, 1993). Southeast Asian Bull. Math. 19 (1995), no. 2, 99–106

17. Martínez-Legaz, J. E.: Generalized convex duality and its economic applications. Handbook of generalized convexity and generalized monotonicity, 237–292, Nonconvex Optim. Appl., 76, Springer, New York, 2005

18. Martínez-Legaz, J.E., Romano-Rodríguez, S.: \( \alpha \)-lower subdifferentiable functions. SIAM J. Optim. 3(4), 800–825 (1993)

    Article  MathSciNet  Google Scholar 

19. Moreau, J.-J.: Inf-convolution, sous-additivité, convexit é des fonctions numériques. (French). J. Math. Pures Appl. 49, 109–154 (1970)

    MathSciNet  MATH  Google Scholar 

20. Pallaschke, D., Rolewicz, S.: Foundations of mathematical optimization. Convex analysis without linearity. Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht (1997)

    MATH  Google Scholar 

21. Passy, U., Prisman, E.Z.: Conjugacy in quasiconvex programming. Math. Program. 30(2), 121–146 (1984)

    Article  MathSciNet  Google Scholar 

22. Passy, U., Prisman, E.Z.: A convexlike duality scheme for quasiconvex programs. Math. Program. 32(3), 278–300 (1985)

    Article  MathSciNet  Google Scholar 

23. Penot, J.-P., Volle, M.: On quasi-convex duality. Math. Oper. Res. 15(4), 597–625 (1990)

    Article  MathSciNet  Google Scholar 

24. Plastria, F.: Lower subdifferentiable functions and their minimization by cutting planes. J. Optim. Theory Appl. 46(1), 37–53 (1985)

    Article  MathSciNet  Google Scholar 

25. Rockafellar, R.T.: Convex analysis. Princeton Mathematical Series. Princeton University Press, Princeton (1970)

    Google Scholar 

26. Rubinov, A.: Abstract Convexity and Global Optimization Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht (2000)

    Book  Google Scholar 

27. Singer, I.: Abstract convex analysis. With a foreword by A. M. Rubinov. Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, (1997)

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