Startseite Mathematik On vector optimality conditions for constrained problems with ℓ-stable data
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

On vector optimality conditions for constrained problems with ℓ-stable data

  • Marie Dvorská EMAIL logo
Veröffentlicht/Copyright: 26. August 2016
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 3

Abstract

The aim of this paper is to enhance certain optimality conditions for constrained vector programming problem with ℓ-stable data published by [GINCHEV, I.: On scalar and vector ℓ-stable functions, Nonlinear Anal. 74 (2011), 182–194], and by [BEDNAŘIK, D.—PASTOR, K.: On second-order condition in constrained vector optimization, Nonlinear Anal. 74 (2011), 1372–1382].

Key words: ℓ-stable function; generalized second-order directional derivative; Dini derivative; local weakly efficient point; isolated local minimizer
MSC 2010: Primary 49K10; 49J52; 49J50; Secondary 90C29; 90C30

This work was supported by the student project PrF-2013-013 of the Palacký University.

(Communicated by Ján Borsík)

Acknowledgement

I would like to express my sincere gratitude to my supervisor, Associate Professor Dr. Karel Pastor, for his advice and helpful discussion.

References

[BP1] Bednařik, D.—Pastor, K.: On second-order conditions in unconstrained optimization, Math. Program. Ser. A 113 (2008), 283–298.10.1007/s10107-007-0094-8Suche in Google Scholar

[BP2] Bednařik, D.—Pastor, K.: ℓ-stable functions are continuous, Nonlinear Anal. 70 (2009), 2317–2324.10.1016/j.na.2008.03.011Suche in Google Scholar

[BP3] Bednařik, D.—Pastor, K.: Decrease ofC{1, 1property in vector optimization, RAIRO Oper. Res. 43 (2009), 359–372.10.1051/ro/2009023Suche in Google Scholar

[BP4] Bednařik, D.—Pastor, K.: On second-order condition in constrained vector optimization, Nonlinear Anal. 74 (2011), 1372–1382.10.1016/j.na.2010.10.009Suche in Google Scholar

[BP5] Bednařik, D.—Pastor, K.: Composition ofℓ-stable vector functions, Math. Slovaca 62 (2012), 995\nbd–1005.10.2478/s12175-012-0060-7Suche in Google Scholar

[DP] Dvorská, M.—Pastor, K.: On comparison ofℓ-stable vector optimization results, Math. Slovaca 64 (2014), 973–990.10.2478/s12175-014-0252-4Suche in Google Scholar

[G] Ginchev, I.: On scalar and vector ℓ-stable functions, Nonlinear Anal. 74 (2011), 182–194.10.1016/j.na.2010.08.032Suche in Google Scholar

[GG] Ginchev, I.—Guerraggio, A.: Second-order conditions for constrained vector optimization problems with ℓ-stable data, Optimization 60 (2011), 179–199.10.1080/02331930903578718Suche in Google Scholar

[J] Jahn, J.: Vector Optimization, Springer-Verlag, Berlin, 2004.10.1007/978-3-540-24828-6Suche in Google Scholar

[KT] Khanh, P. Q.—Tuan, N. D.: Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives, J. Optim. Theory Appl. 133 (2007), 341–357.10.1007/s10957-007-9169-1Suche in Google Scholar

[L] Lebourg, G.: Generic differentiability of Lipschitz functions, Trans. Amer. Math. Soc. 256 (1979), 125\nbd–144.10.1090/S0002-9947-1979-0546911-1Suche in Google Scholar

Received: 2012-11-13
Accepted: 2013-10-28
Published Online: 2016-8-26
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
  16. A construction of a Peano curve
  17. Research Article
  18. Compositions of ϱ-upper continuous functions
  19. Research Article
  20. Products of Świa̧tkowski functions
  21. Research Article
  22. Subclasses of meromorphically p-valent functions involving a certain linear operator
  23. Research Article
  24. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
  25. Research Article
  26. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales
  27. Research Article
  28. On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
  29. Research Article
  30. Meromorphic solutions of q-shift difference equations
  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
  35. Research Article
  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
  37. Research Article
  38. The local spectral radius of a nonnegative orbit of compact linear operators
  39. Research Article
  40. A note on Lie product preserving maps on Mn(ℝ)
  41. Research Article
  42. On vector optimality conditions for constrained problems with ℓ-stable data
  43. Research Article
  44. Reparameterization of weakly nonlinear regression models with constraints
  45. Research Article
  46. Convolutions of polynomial kernels
  47. Research Article
  48. Closed form evaluation of sums containing squares of Fibonomial coefficients
https://doi.org/10.1515/ms-2015-0174
Schlagwörter für diesen Artikel
ℓ-stable function; generalized second-order directional derivative; Dini derivative; local weakly efficient point; isolated local minimizer

Artikel in diesem Heft

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
  16. A construction of a Peano curve
  17. Research Article
  18. Compositions of ϱ-upper continuous functions
  19. Research Article
  20. Products of Świa̧tkowski functions
  21. Research Article
  22. Subclasses of meromorphically p-valent functions involving a certain linear operator
  23. Research Article
  24. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
  25. Research Article
  26. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales
  27. Research Article
  28. On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
  29. Research Article
  30. Meromorphic solutions of q-shift difference equations
  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
  35. Research Article
  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
  37. Research Article
  38. The local spectral radius of a nonnegative orbit of compact linear operators
  39. Research Article
  40. A note on Lie product preserving maps on Mn(ℝ)
  41. Research Article
  42. On vector optimality conditions for constrained problems with ℓ-stable data
  43. Research Article
  44. Reparameterization of weakly nonlinear regression models with constraints
  45. Research Article
  46. Convolutions of polynomial kernels
  47. Research Article
  48. Closed form evaluation of sums containing squares of Fibonomial coefficients
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0174/pdf
Button zum nach oben scrollen