Vectorial optimization in locally convex spaces ordered by supernormal cones and extensions

Vasile Postolică

doi:10.33993/jnaat292-668

Authors

Vasile Postolică Department of Mathematics Piatra Neamt, Romania

DOI:

https://doi.org/10.33993/jnaat292-668

Abstract views: 195

Abstract

Not available.

Downloads

Download data is not yet available.

References

Bahya, A. O., Ensembles coniquement bornés et cônes nucléaires dans les espaces Iocalement convexes séparés. Thesis (Docteur de 3-ème cycle) École Normale Supérieure, Takaddoum Rabat, Maroc, 1989.

Bahya, A. O., Étude des cônes nucléaires, Ann. Sci. Math. Québec, 15, no. 2,pp. 123-134, 1992.

Bakhtin, I.A., Cones in Banach spaces, Voronezh (in Russian), 1977.

Ha, T. X. D., On the existence of efficient points in locally convex spaces, Journal of Global Optimization, Kluwer Academic Publishers Dordrecht, The Netherlands (to appear),1993. https://doi.org/10.1007/bf01098361 DOI: https://doi.org/10.1007/BF01098361

Ha, T. X. D., A note on a class of cones ensuring the existence of efficient points ,in bounded complete sets, Journal Optimization, Gordon and Breach Science Publishers SA, Yverdon, Switzerland (to appear), 1993. https://doi.org/10.1080/02331939408844011 DOI: https://doi.org/10.1080/02331939408844011

Hiriart-Urruty, J.B., From convex optimization to non-convex optimization. Part I: Necessary and sufficient conditions for global optimality, Nonsmooth Optimization and Related Topics, F. H. Clarke, V. F. Demyanov, F. Giannesse, Editors, Plenum, 1989, https://doi.org/10.1007/978-1-4757-6019-4_13 DOI: https://doi.org/10.1007/978-1-4757-6019-4_13

Isac, G., Points critiques pour des systèmes dynamiques. Cônes nucléaires et optimum de Pareto, Preprint, Royal Military College of St. Jean, Québec, Canada, 1981.

Isac, G., Sur l'existence de I'optimum de Pareto, Riv. Mat. Univ. Parma,4, no.9, pp. 303-325, 1983.

Isac, G" Un critère de sommabilité absolue dans les espaces locaIement convexes or-donnés. Cônes nucléaires, Mathematica, (25) 48, no.2, pp.159-169, 1983.

Isac, G., Supernormal cones and absolute summability, Libertas Math., 5, pp.17-31, 1985.

Isac, G., Supernormal cones and fixed point theory,Rocky Mountain J. Math., 17, no. 3, pp. 219-226, 1987, https://doi.org/10.1216/rmj-1987-17-2-219 DOI: https://doi.org/10.1216/RMJ-1987-17-2-219

Isac, G., Pareto optimization in infinite dimensional spaces. The importance of nuclear cones, Report at The FourthSsIAM Conference on Optimization, May 11-13, Chicago, U.S.A., 23 pag., 1992.

Isac, G., Postolică, V., The Best Approximation and, Optimization in Locally Convex Spaces, Verlag Peter Lang GmbH, Frankfurt am Mai, Germany, 1993.

Jahn, J., A generalization oifa theorem of Arrow, Barankin and Blockwell, SIAM J. Control and Optimization, 26, no. 5, pp. 999-1005, 1988, https://doi.org/10.1137/0326055 DOI: https://doi.org/10.1137/0326055

Krasnoselski, M. A.,Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.

Luc, D. T., Theory of Vector Optimization, Lecture Notes in Economics and Math.Syst., no.319, Springer-Verlag, Berlin, 1989, https://doi.org/10.1007/978-3-642-50280-4 DOI: https://doi.org/10.1007/978-3-642-50280-4

J Németh, A. B., Between Pareto efficiency and, Pareto ε-efficiency Optimization, 20, no. 5, pp. 615-692, 1989. DOI: https://doi.org/10.1080/02331938908843483

Pietch, A., Nuclear Locally ConvexSspaces, Springer-Verlag, New York / Berlin, 1972.

Pontini, C., Inclusion theorems for non-explosive and strongly exposed cones in normes spaces, J. Math. Anal. Appl., 148, pp. 275-286, 1990, https://doi.org/10.1016/0022-247x(90)90001-v DOI: https://doi.org/10.1016/0022-247X(90)90001-V

Postolică, V., Vectorial optimizations programs with multifunctions and duality, Ann. Sci. Math. Québec, 10, no.1, pp.85-102, 1986.

Postolică, V., A generalization of Fenchel's duality theorem, Ann. Sci. Math. Québec, 10, no. 2, pp. 199-206, 1986.

J Postolică, V., Some existence results concerning the efficient points in locally convex spaces, Babeş-Bolyai Univ., Faculty of Math., Seminar on Math. Anal., no. 7, pp. 75-80, 1987.

Postolică, V., Existence results for the efficient points in locally convex spaces ordered, by supernormal cones and conically bounded sets Babeş-Bolyai Univ., Faculty of Math. Seminar on Math. Anal., no. 7, pp. 187-192, 1988.

Postolică, V., Existence ,conditions of efficient points for multifunctions with values in locallz convex spaces, Stud. Cerc. Mat., 41, no.4, pp. 325-339, 1989.

Postolică, V., On ε-vectorial subdifferential and applications. Communication to the 12th Seminar on Ordered Topological Vector Spaces, Sinaia, Romania, June, 25-27, 1991.

Postolică, V., New existence results for efficient points in locally convex spaces ordered bz supernormal cones, Journal of Global Optimizaiton, Kluwer Academic Publisher, Dordrecht, The Netherlands, pp. 233-242, 1993, https://doi.org/10.1007/bf01096741 DOI: https://doi.org/10.1007/BF01096741

Postolică, V., An extension to sets of supernormal cones and generalized subdifferentials, Journal Optimization, Gordon and Breach Science Publisher SA, Yverdon, Switzerland, 29, no.2, pp.131-139, 1994, https://doi.org/10.1080/02331939408843942 DOI: https://doi.org/10.1080/02331939408843942

Precupanu, Th., Espaces linéaires à semi-normes hilbertiennes, An. St. Univ. ,"Al. I. Cuza", Iaşi, 15, pp. 83-99, 1969.

Precupanu, Th., Scalar minimax properties in vectorial optimization. International Series of Numerical Mathematics, Birkhäuser Verlag, Basel, Ijmuiden, The Netherlands, 107, pp. 299-306, 1992, https://doi.org/10.1007/978-3-0348-8625-3_27 DOI: https://doi.org/10.1007/978-3-0348-8625-3_27

Sterna-Karwat, A., On the existence of cone maximal points in real toporogical linear spaces, Israel Journal of Mathematics, 54, no. 1, pp. 33-41, 1986, https://doi.org/10.1007/bf02764874 DOI: https://doi.org/10.1007/BF02764874