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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3


On vector optimality conditions for constrained problems with -stable data

Marie Dvorská
  • Department of Mathematical Analysis and Applications of Mathematics Faculty of Science Palacký University Tř. 17. listopadu 12 772 00 Olomouc CZECH REPUBLIC
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Published Online: 2016-08-26 | DOI: https://doi.org/10.1515/ms-2015-0174


The aim of this paper is to enhance certain optimality conditions for constrained vector programming problem with -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.


  • [BP1]

    Bednařik, D.—Pastor, K.: On second-order conditions in unconstrained optimization, Math. Program. Ser. A 113 (2008), 283–298.Google Scholar

  • [BP2]

    Bednařik, D.—Pastor, K.: -stable functions are continuous, Nonlinear Anal. 70 (2009), 2317–2324.Google Scholar

  • [BP3]

    Bednařik, D.—Pastor, K.: Decrease of C{1, 1 property in vector optimization, RAIRO Oper. Res. 43 (2009), 359–372.Google Scholar

  • [BP4]

    Bednařik, D.—Pastor, K.: On second-order condition in constrained vector optimization, Nonlinear Anal. 74 (2011), 1372–1382.Google Scholar

  • [BP5]

    Bednařik, D.—Pastor, K.: Composition of -stable vector functions, Math. Slovaca 62 (2012), 995\nbd–1005.Google Scholar

  • [DP]

    Dvorská, M.—Pastor, K.: On comparison of -stable vector optimization results, Math. Slovaca 64 (2014), 973–990.Google Scholar

  • [G]

    Ginchev, I.: On scalar and vector -stable functions, Nonlinear Anal. 74 (2011), 182–194.Google Scholar

  • [GG]

    Ginchev, I.—Guerraggio, A.: Second-order conditions for constrained vector optimization problems with ℓ-stable data, Optimization 60 (2011), 179–199.Google Scholar

  • [J]

    Jahn, J.: Vector Optimization, Springer-Verlag, Berlin, 2004.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.Google Scholar

  • [L]

    Lebourg, G.: Generic differentiability of Lipschitz functions, Trans. Amer. Math. Soc. 256 (1979), 125\nbd–144.Google Scholar

About the article

Received: 2012-11-13

Accepted: 2013-10-28

Published Online: 2016-08-26

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 721–730, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0174.

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