Maximal pseudomonotonicity of generalized subdifferentials of explicitly quasiconvex functions

Abstract

??

Authors

Radu Precup
”Babeș-Bolyai” University Department of Mathematics, Cluj-Napoca, Romania

Keywords

PDF

Cite this paper as:

R. Precup, Maximal pseudomonotonicity of generalized subdifferentials of explicitly quasiconvex functions, Rev. Anal. Numér. Théor. Approx., 17 (1988) no. 1, pp. 53-62.

About this paper

Journal

Mathematica-Revue d`analyse numérique et de théorie d`approximation

Publisher Name

Academia Republicii S.R.

Print ISSN

Not available yet.

Online ISSN

Not available yet.

MR: 90a:90215.

References

[1] Barbu, V., Precupanu, Th., Convexity and optimization in Banach spaces. Revised edition. Translated from the Romanian. Editura Academiei, Bucharest; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1978. xi+316 pp. ISBN: 90-286-0018-3, MR0513634.

[2] Behringer, F. A., More on Karamardian’s theorem concerning the quasiconvexity of strictly quasiconvex functions. Z. Angew. Math. Mech. 60 (1980), no. 7, T335-T338, MR0623899.

[3] Crouzeix, Jean-Pierre, 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 Mathématiques. Série: E, No. d’Ordre 250. Université de Clermont-Ferrand II, Clermont-Ferrand, 1977. v+ 231 pp., MR0484417.

[4] Evans, J. P.; Gould, F. J. Stability in nonlinear programming. Operations Res. 18 1970 107-118, MR0264984, https://doi.org/10.1287/opre.18.1.107

[5] Greenberg, Harvey J., Pierskalla, William P., Quasi-conjugate functions and surrogate duality. Cahiers Centre Études Recherche Opér. 15 (1973), 437-448, MR0366402.

[6] Karamardian, S., Strictly quasi-convex (concave) functions and duality in mathematical programming. J. Math. Anal. Appl. 20 1967 344-358, MR0219315, https://doi.org/10.1016/0022-247x(67)90095-9

[7] Karamardian, S. Complementarity problems over cones with monotone and pseudomonotone maps. J. Optimization Theory Appl. 18 (1976), no. 4, 445-454, MR0472053, https://doi.org/10.1007/bf00932654

[8] Kolumbán, Iosif(R-CLUJ), Über die Stetigkeit quasikonvexer Funktionen. (German) [On the continuity of quasiconvex functions] Itinerant seminar on functional equations, approximation and convexity (Cluj-Napoca, 1983), 83-84, Preprint, 83-2, Univ. “Babeş-Bolyai”, Cluj-Napoca, 1983, MR0750497.

[9] Pascali, Dan; Sburlan, Silviu Nonlinear mappings of monotone type. Martinus Nijhoff Publishers, The Hague; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1978. x+341 pp. ISBN: 90-286-0118-*, MR0531036.

[10] Popoviciu, Tiberiu Deux remarques sur les fonctions convexes. (French) Bull. Sect. Sci. Acad. Roum. 20 (1938), 187-191 (or 45-49) (1939), MR0000418.

[11] Precup, R., Continuity of quasiconvex fucntionals and of hemimonotone nonlinear operators, Seminarul itinerant de ec.funcţ. aprox. şi convex., Cluj-Napoca, 1982, pp. 297-302.

[12] Precup, Radu, Quasiconvexity, generalized subdifferential and pseudomonotone mappings. Itinerant Seminar on Functional Equations, Approximation and Convexity (Cluj-Napoca, 1987), 261–272, Preprint, 87-6, Univ. “Babeş-Bolyai”, Cluj-Napoca, 1987, MR0993543.

[13] Rockafellar, R. Tyrrell Convex analysis. Princeton Mathematical Series, No. 28 Princeton University Press, Princeton, N.J. 1970 xviii+451 pp., MR0274683.

[14] Zabotin, Y.I., Korablev, A.I., Khabibullin, R.F., Conditions for an extremum of a functional in case of constraints, cybernetics, 9, pp. 982-988 (1975), https://doi.org/10.1007/bf01071680

Related Posts

Menu