Skip to main content
SpringerLink
Log in

Non-linear separation theorems, duality and optimality conditions

  • Conference paper
  • First Online:
Optimization and Related Fields

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1190))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.Avriel. ‘Non linear programming. Analysis and methods'. Prentice Hall, (1976).

    Google Scholar 

  2. M.S.Bazaraa, C.M.Shetty. ‘Foundations of optimizations'. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag(1976).

    Google Scholar 

  3. M.S. Bazaraa. ‘A theorem of the alternative with applications to convex programming: optimality, duality and stability'. J. of Math. Analysis and Appl., vol.41, (1973), 701–715.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Ben-Israel, A. Ben-Tal, and S. Zlobec. ‘Optimality in nonlinear programming. A feasible directions approach'. J.Wiley, New York, (1981).

    MATH  Google Scholar 

  5. A. Ben-Israel, A. Charnes, and K.O. Kortanek. ‘Asymptotic duality over closed convex sets'. J. Math. Analysis Appl., vol.35, (1971),677–691.

    Article  MathSciNet  MATH  Google Scholar 

  6. C.Beoni. ‘A generalization of Fenchel duality theory'. Jou Optimization Th. Appl., vol.49, N.3, June 1986.

    Google Scholar 

  7. G.R. Bitran, T. Magnanti. ‘The structure of admissible points with respect to Cone Dominance'. J.O.T.A., vol.29, n.4, (1979),573–614.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Calligaris, P. Oliva. ‘Necessary and sufficient conditions for Pareto problems'. Boll. UMI (5), 18B (1981), 177–216.

    MathSciNet  MATH  Google Scholar 

  9. A.Cambini, L.Martein. 'separation functions and optimality conditions in vector extremum problems'. Technical report A-120, Dept. of Math., Univ. of Pisa.

    Google Scholar 

  10. A.Y. Dubovitskii and A.A. Milyutin. ‘The extremum problem in the presence of constraints'. Doklady Akademiie Nauk SSSR, vol.149,(1963), 759–762.

    MATH  Google Scholar 

  11. E.Eisenberg. ‘On cone functions'. In "Recent advances in mathematical programming". P.Wolfe and R.L.Graves (eds.), McGraw-Hill,(1963), 27–33

    Google Scholar 

  12. K.H.Elster, R.Nehse. ‘Optimality conditions for some non — convex problems'. Lecture Notes in Control and Information Sciences, n.23, Springer-Verlag, (1980).

    Google Scholar 

  13. H. Everett. ‘Generalized Lagrange multiplier method for solving problems of optimum allocation of resources'. Oper. Res., vol.11,(1963), 399–417.

    Article  MathSciNet  MATH  Google Scholar 

  14. A.V. Fiacco,and G.P. McCormick. ‘Nonlinear programming: sequential unconstrained minimization techniques'. J. Wiley, New York, (1968).

    MATH  Google Scholar 

  15. F. Giannessi. ‘Theorems of alternative, quadratic programs and complementarity problems'. In "Variational inequalities and complementarity problems". Cottle-Giannessi-Lions (eds), J.Wiley, New York, (1980), 151–186.

    Google Scholar 

  16. F.Giannessi. ‘Theorems of the alternative and optimality conditions'. J.O.T.A., vol.42, n.3, March (1984).

    Google Scholar 

  17. F.Giannessi. ‘On Lagrangian non-linear multipliers theory for constrained optimization and related topics'. Dept. Math., Appl.Math. Sect. (Optimization Group), Res. Report n.123, (1984).

    Google Scholar 

  18. F.J. Gould. ‘Extensions of Lagrange multipliers in nonlinear programming'. SIAM J. Applied Math., vol.17, (1969), 1280–1297.

    Article  MathSciNet  MATH  Google Scholar 

  19. F.J. Gould. ‘Nonlinear pricing: applications to concave programming'. Operat. Research, vol.19, n.4, (1971), 1026–1035.

    Article  MathSciNet  MATH  Google Scholar 

  20. S.P. Han, and O.L. Mangasarian. ‘Exact penalty functions in nonlinear programming'. Math. Programming, vol.17, (1979), 251–269.

    Article  MathSciNet  MATH  Google Scholar 

  21. M.Hayashi, H.Komiya. ‘Perfect duality for Convexlike programs'. J.O.T.A., vol.38, n.2 (1982).

    Google Scholar 

  22. V.Jeyakumar. ‘Convexlike alternative theorems and mathematical programming'. Dept. Math., Univ. of Melbourne, Res.Rep. n.13,(1984). To appear on "Optimization, Mathematische Operationsforschung und Statistik".

    Google Scholar 

  23. L. McLinden. ‘Duality theorems and theorem of the alternative'. Proc. Ann. Math. Soc., vol.53, n.1, (1975), 172–175.

    Article  MathSciNet  MATH  Google Scholar 

  24. O.L. Mangasarian. ‘Nonlinear programming'. McGraw-Hill, New York, (1969).

    MATH  Google Scholar 

  25. L.Martein. ‘Regularity conditions for constrained extremum problems'. Jou.Optimization Th.Appl., vol.47,N.2,Oct.1985.

    Google Scholar 

  26. L.Martein. ‘A necessary and sufficient regularity condition for convex extremum problems'. Technical Report A-90, Dept. of Math., Univ. of Pisa.

    Google Scholar 

  27. L.Martein. 'sulla separabilità locale in problemi di estremo vincolato'. Proceed. of the VI Meeting "Associazione per la Matematica Applicata alle Scienze Economiche e Sociali", (1982).

    Google Scholar 

  28. L.Martein. 'sulla dualità lagrangiana esponenziale'. Technical Report A-114, Dept. of Math., Univ. of Pisa.

    Google Scholar 

  29. M.Pappalardo. ‘On the duality gap in non convex optimization'. Mathematics of Operations Research (to appear).

    Google Scholar 

  30. R.T.Rockafellar. ‘Convex Analysis'. Princeton, (1970).

    Google Scholar 

  31. R.T. Rockafellar. ‘Penalty methods and augmented Lagrangians in nonlinear programming'. Proceedings of 5-th Conference on Optim.Tech., Springer-Verlag, Berlin, (1973), 418–425.

    Google Scholar 

  32. R.T. Rockafellar. ‘Augmented Lagrange multiplier functions and duality in nonconvex programmin'. SIAM J. on Control, vol.12, (1974), 268–283.

    Article  MathSciNet  MATH  Google Scholar 

  33. F.Tardella. ‘On the image of a constrained extremum problems'.Tech. Report A-106, Dept. of Math., Univ. of Pisa.

    Google Scholar 

  34. J. Tind, and L.A. Wolsey. ‘An elementary survey of general duality theory'. Mathematical Programming, vol.21, n.3, (1981),241–261.

    Article  MathSciNet  MATH  Google Scholar 

  35. F.Tardella. (private communication).

    Google Scholar 

Download references

Authors
  1. A. Cambini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Roberto Conti Ennio De Giorgi Franco Giannessi

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Cambini, A. (1986). Non-linear separation theorems, duality and optimality conditions. In: Conti, R., De Giorgi, E., Giannessi, F. (eds) Optimization and Related Fields. Lecture Notes in Mathematics, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076702

Download citation

  • DOI: https://doi.org/10.1007/BFb0076702

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16476-0

  • Online ISBN: 978-3-540-39817-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation