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Derivatives of Hadamard type in vector optimization

  • Karel Pastor EMAIL logo
Published/Copyright: March 31, 2018
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 2

Abstract

In our paper we will continue the comparison which was started by Vsevolod I. Ivanov [Nonlinear Analysis 125 (2015), 270–289], where he compared scalar optimality conditions stated in terms of Hadamard derivatives for arbitrary functions and those which was stated for ℓ-stable functions in terms of Dini derivatives. We will study the vector optimization problem and we show that also in this case the optimality condition stated in terms of Hadamard derivatives is more advantageous.

Keywords: C1,1-function; ℓ-stable function; generalized second-order derivative; optimality conditions
MSC 2010: 49K10; 49J52; 49J50; 90C29; 90C30

Communicated by Anatolij Dvurečenskij

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Received: 2016-1-12
Accepted: 2016-9-26
Published Online: 2018-3-31
Published in Print: 2018-4-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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  6. On lattices of z-ideals of function rings
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  14. On the alexander dual of path ideals of cycle posets
  16. Generalized multiplicative derivations in 3-prime near rings
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  24. Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
  26. Positive periodic solutions for singular high-order neutral functional differential equations
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  30. Matrix mappings and general bounded linear operators on the space bv
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https://doi.org/10.1515/ms-2017-0113
Keywords for this article
C1,1-function; ℓ-stable function; generalized second-order derivative; optimality conditions

Articles in the same Issue

  2. On the family of functions with closure of graphs in the Mendez ideals
  4. The predicate completion of a partial information system
  6. On lattices of z-ideals of function rings
  8. Compactifications of partial frames via strongly regular ideals
  10. Lifting components in clean abelian ℓ-groups
  12. Invariance of nonatomic measures on effect algebras
  14. On the alexander dual of path ideals of cycle posets
  16. Generalized multiplicative derivations in 3-prime near rings
  18. Cleft extensions for quasi-entwining structures
  20. Groups with positive rank gradient and their actions
  22. Certain results on q-starlike and q-convex error functions
  24. Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
  26. Positive periodic solutions for singular high-order neutral functional differential equations
  28. A special class of functional equations
  30. Matrix mappings and general bounded linear operators on the space bv
  32. Skew-symmetric operators and reflexivity
  34. Derivatives of Hadamard type in vector optimization
  36. Cardinal functions of the hyperspace of convergent sequences
  38. Suzuki-type of common fixed point theorems in fuzzy metric spaces
  40. Second hankel determinat for certain analytic functions satisfying subordinate condition
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