Skip to main content
SpringerLink
Log in

Full Nuclear Cones and a Relation Between Strong Optimization and Pareto Efficiency

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this paper we present some new and pertinent connections between the Strong Optimization and the Approximate Pareto type Efficiency, in particular, with the usual Vector Optimization, at first in the Ordered Vector Spaces by the natural Convex Cones and, afterwards, in the Ordered Hausdorff Locally Convex Spaces. The main result is obtained considering the notion of full nuclear cone. Our results, is related to an appropriate scalarization method

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bahya A.O. (1989). Ensembels coniquement bornes et cônes nucléaires dans les espaces locallement conexes, séparés, These (Docteur de 3-eme cycle), Ecole Normale Supéirieure, Takaddoum, Rabat, Maroc (Morocco)

  2. A.O. Bahya (1992) ArticleTitleEtude des cônes nucleaires Ann. Sci. Math. Québec 15 IssueID2 123–134

    Google Scholar 

  3. Bahya A.O. (1997). Etude des cônes nucléaires dans les espaces localement convex séparés, These de Docteur d’Etat, Faculté des Sciences de Rabat, Maroc (Morocco)

  4. T. Cardinali F. Papalini (1994) ArticleTitleFixed point theorems for multifunctions in topological vector spaces J. Mathematical Analysis and Applications 186 769–177 Occurrence Handle10.1006/jmaa.1994.1332

    Article  Google Scholar 

  5. F.M. El Mounir M. Oudades (2000) ArticleTitleApplications relativement bornées sur les cônes C-reguliers Ann. Sci. Math. Québec 24 IssueID1 53–61

    Google Scholar 

  6. Hyers D.H., Isac G., Rassias Th.M. (1997). Topics in Nonlinear Analysis and Applications, World Scientific

  7. G. Isac (1981) Points Critiques des Systémes Dynamiques, Cônes Nucléaires et Optimum de Pareto, Research report Royal Military College of St. Jean Québec, Canada

    Google Scholar 

  8. G. Isac (1983) ArticleTitleSur l’existence de l’optimum de Pareto Riv. Mat Univ. Parma 9 IssueID4 303–325

    Google Scholar 

  9. G. Isac (1983) Un critere de sommabilité dans les espaces locallement convexes ordonnes: Cônes nucléaires, Mathematica 25 IssueID48–92 159–169

    Google Scholar 

  10. G. Isac (1985) ArticleTitleSupernormal cones and absolute summability Liberatas Math 5 17–31

    Google Scholar 

  11. G. Isac (1987) ArticleTitleSupernormal cones and fixed-point theory Rocky Mountain J. Math 17 IssueID3 219–226

    Google Scholar 

  12. G. Isac (1994) ArticleTitlePareto optimization in infinite dimensional spaces: the importance of nuclear cones J. Math. Anal. and Appl 182 IssueID2 393–404 Occurrence Handle10.1006/jmaa.1994.1093

    Article  Google Scholar 

  13. G. Isac (1997) ArticleTitleEkeland’s principle and nuclear cones: a geometrical aspect Math. Comput. Modeling 26 IssueID11 111–116 Occurrence Handle10.1016/S0895-7177(97)00223-9

    Article  Google Scholar 

  14. Isac G. (2002). On Pareto efficiency. A general constructive existence principle, In: Pardalo, P.M., Migdalas, A. and Burkard, R. (eds.), Combinatorial and Global Optimization, Kluwer Academic Publishers, pp. 133–144.

  15. G. Isac A.O. Bahya (2002) ArticleTitleFull nuclear cones assocaited to a normal cone Application to Pareto efficiency. Applied Mathematics Letters 15 633–639 Occurrence Handle10.1016/S0893-9659(02)80017-9

    Article  Google Scholar 

  16. Isac G., Bulavski V.A., Kalashnikov V.V. (2002), Complementarity, Equilibrium, Efficienecy and Economics, Kluwer Academic Publishers

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

    Google Scholar 

  18. Isac, G. and Tammer, Chr. (2002), Nuclear and full nuclear cones in product spaces. Pareto efficiency and an Ekeland type variational principle (Preprint).

  19. Luc, D.T. (1989), Theory of Vector Optimization, Lecture notes in Economics and Mathematical Systems, Nr. 319, Springer-Verlag.

  20. A.B. Németh (1989) ArticleTitleBetween Pareto efficiency and Pareto ɛ-efficiency Optimization 20 IssueID5 615–637

    Google Scholar 

  21. M. Petschke (1990) ArticleTitleOn a theorem of Arrow, Barankin and Blackewell SIAM J. Control Opt 28 IssueID2 395–401 Occurrence Handle10.1137/0328021

    Article  Google Scholar 

  22. V. Postolică (1981) ArticleTitleSpline functions in H-locally convex spaces An. st. Univ. Al. I. Cuza lasi, Romania 27 333–338

    Google Scholar 

  23. V. Postolică (1993) ArticleTitleNew existence results for efficient points in locally convex spaces ordered by supernormal cones J. Global Optimization 3 233–242 Occurrence Handle10.1007/BF01096741

    Article  Google Scholar 

  24. V. Postolică (1995) ArticleTitleProperties of Pareto set in locally convex spaces Optimization 34 223–229

    Google Scholar 

  25. Postolică V. Properties of Efficient points sets and related topics. In: Cabalbero R., Ruiz F., Steuer R.E (eds). Advances in Multiple Objective and Goal Programming. Lecture Notes in Economics and Mathematical Systems 455, Springer-Verlag.

  26. Postolică, V. (2002), Efficiency and Choquet boundaries in separated locally convex spaces, (Preprint) (Submitted)

  27. Th. Precupanu (1969) ArticleTitleEspaces linéaires à semi-normes hilbertiennes An. Şt. Univ. Al. I. Cuza Iasi, Romania 15 83–93

    Google Scholar 

  28. Th. Precupanu (1992) ArticleTitleScalar minimax properties in vectorial optimization International Series of Numerical Mathematics 107 299–306

    Google Scholar 

  29. F. Treves (1967) Locally Convex Spaces and Linear Partial Differential Equations Springer Verlag New-York

    Google Scholar 

  30. X.D.H. Truong (1994) ArticleTitleA note on a class of cones ensuring the existence of efficient points in bounded complete sets Optimization 31 141–152

    Google Scholar 

  31. X.D.H. Truong (1994) ArticleTitleOn the existence of efficient points in locally convex spaces J. Global Optimization 4 265–278 Occurrence Handle10.1007/BF01098361

    Article  Google Scholar 

  32. Turinici M. (1994). Vector extensions of the variational Ekeland’s Result, Ann. St. Univ. Al. I. Cuza, Iasi Romania, Tom XL, Matematica F-3, 225–266.

Download references

Author information

Authors and Affiliations

  1. Department of mathematics, Royal Military College of Canada, P.O. Box 17000, STN,Forces Kingston, Ontario, K7K7B4, Canada

    G. Isac

  2. Romanian Academy of Scientists, Department of Mathematical Sciences B-dul Traian nr. 11, Bacău State University, bl. Al, sc. A, apt.13, 5600, Piatra Neamt, Romania

    Vasile Postolică

Authors
  1. G. Isac
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vasile Postolică
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Isac.

Additional information

Mathematics Subject Classification (2000). 90C29

Rights and permissions

Reprints and permissions

About this article

Cite this article

Isac, G., Postolică, V. Full Nuclear Cones and a Relation Between Strong Optimization and Pareto Efficiency. J Glob Optim 32, 507–516 (2005). https://doi.org/10.1007/s10898-003-2687-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-003-2687-y

Keywords

Search

Navigation