Research Article

Year 2021,
Volume: 4 Issue: 3, 163 - 170, 30.09.2021
### Abstract

### References

- Q. H. Ansari, E. K¨obis, P. K. Sharma, Characterizations of multiobjective robustness via oriented distance function and image space analysis, J. Optim. Theory. Appl., 181(3) (2019), 817-839.
- J. Chen, Q. H. Ansari, J.-C. Yao, Characterizations of set order relations and constrained set optimization problems via oriented distance function, Optimization, 66(11) (2017), 1741-1754.
- G. P. Crespi, I. Ginchev, M. Rocca, First-order optimality conditions in set-valued optimization, Math. Meth. Oper. Res., 63(1) (2006), 87-106.
- E. Hern´andez, L. Rodr´ıguez-Mar´ın, Nonconvex scalarization in set optimization with set-valued maps, J. Math. Anal. Appl., 325(1) (2007), 1-18.
- J. B. Hiriart-Urruty, Tangent cone, generalized gradients and mathematical programming in Banach spaces, Math. Oper. Res., 4(1) (1979), 1-97.
- J. Jahn, T. X. D. Ha, New order relations in set optimization, J. Optimiz. Theory. App., 148(2) (2011), 209-236.
- B. Jim´enez, V. Novo, A. V´ılchez, Characterization of set relations through extensions of the oriented distance, Math. Method. Oper. Res., 91 (2020), 89-115.
- A. A. Khan, C. Tammer, C. Z˘alinescu, Set-valued Optimization: An Introduction with Applications, Springer-Verlag, Berlin, 2015.
- E. Karaman, G¨omme fonksiyonu kullanılarak k¨ume optimizasyonuna g¨ore verilen k¨ume de˘gerli optimizasyon problem- lerinin optimallik kos¸ulları, S¨uleyman Demirel ¨Universitesi Fen Edebiyat Fak¨ultesi Fen Dergisi, 14 (2019), 105-111.
- E. Karaman, Nonsmooth set variational inequality problems and optimality criteria for set optimization, Miskolc. Math. Notes., 21(1) (2020), 229-240.
- E. Karaman, M. Soyertem, ˙I.Atasever G¨uvenc¸, Optimality conditions in set-valued optimization problem with respect to a partial order relation via directional derivative, Taiwan. J. Math., 24(3) (2020), 709-722.
- E. Karaman, ˙I. Atasever G¨uvenc¸, M. Soyertem, D.Tozkan, M. K¨uc¸¨uk, Y. K¨uc¸¨uk, , A vectorization for nonconvex set- valued optimization, Turk. J. Math., 42 (2018), 1815-1832.
- E. Karaman, M. Soyertem, ˙I. Atasever G¨uvenc¸, D. Tozkan, M. K¨uc¸¨uk, Y. K¨uc¸¨uk, Partial order relations on family of sets and scalarizations for set optimization, Positivity, 22(3) (2018), 3783-802.
- E. Karaman, ˙I. Atasever G¨uvenc¸, M. Soyertem, Optimality conditions in set-valued optimization problems with respect to a partial order relation by using subdifferentials, Optimization, 70(3) (2021) 613-630.
- Khushboo, C. S. Lalitha, Scalarizations for a set optimization problem using generalized oriented distance function, Positivity, 23(5) (2019), 1195-1213.
- D. Kuroiwa, The natural criteria in set-valued optimization, RIMS Kokyuroku, 1031(2) (1998), 85-90.
- D. Kuroiwa, On set-valued optimization, Nonlinear. Anal-Theor., 47(2) (2001), 1395-1400.
- D. Kuroiwa, Existence theorems of set optimization with set-valued maps, J. Inf. Optim. Sci., 24(1) (2003), 73-84.
- D. Kuroiwa, T. Tanaka, T. X. D. Ha, On cone convexity of set-valued maps, Nonlinear. Anal-Theor., 30(3) (1997), 1487- 1496.
- D. Pallaschke, R. Urba´nski, Pairs of Compact Convex Sets, Kluwer Academic Publishers, Dordrecht, (2002).
- M. Pilecka, Optimality conditions in set-valued programming using the set criterion, Thecnical University of Freiberg, 2014 (2014).
- R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, Cambridge, 1993.
- Y. D. Xu, S. J. Li, A new nonlinear scalarization function and applications, Optimization, 65(1) (2016), 207-231.

Year 2021,
Volume: 4 Issue: 3, 163 - 170, 30.09.2021
### Abstract

### References

A new relation on the subset of the space is defined via l-difference in this work. This is a pre-order relation on the family of nonempty sets. Some relations between this pre-order relation and well-known order relations are investigated. Also, solution points of a set-valued optimization problem via set and vector approaches are examined.

- Q. H. Ansari, E. K¨obis, P. K. Sharma, Characterizations of multiobjective robustness via oriented distance function and image space analysis, J. Optim. Theory. Appl., 181(3) (2019), 817-839.
- J. Chen, Q. H. Ansari, J.-C. Yao, Characterizations of set order relations and constrained set optimization problems via oriented distance function, Optimization, 66(11) (2017), 1741-1754.
- G. P. Crespi, I. Ginchev, M. Rocca, First-order optimality conditions in set-valued optimization, Math. Meth. Oper. Res., 63(1) (2006), 87-106.
- E. Hern´andez, L. Rodr´ıguez-Mar´ın, Nonconvex scalarization in set optimization with set-valued maps, J. Math. Anal. Appl., 325(1) (2007), 1-18.
- J. B. Hiriart-Urruty, Tangent cone, generalized gradients and mathematical programming in Banach spaces, Math. Oper. Res., 4(1) (1979), 1-97.
- J. Jahn, T. X. D. Ha, New order relations in set optimization, J. Optimiz. Theory. App., 148(2) (2011), 209-236.
- B. Jim´enez, V. Novo, A. V´ılchez, Characterization of set relations through extensions of the oriented distance, Math. Method. Oper. Res., 91 (2020), 89-115.
- A. A. Khan, C. Tammer, C. Z˘alinescu, Set-valued Optimization: An Introduction with Applications, Springer-Verlag, Berlin, 2015.
- E. Karaman, G¨omme fonksiyonu kullanılarak k¨ume optimizasyonuna g¨ore verilen k¨ume de˘gerli optimizasyon problem- lerinin optimallik kos¸ulları, S¨uleyman Demirel ¨Universitesi Fen Edebiyat Fak¨ultesi Fen Dergisi, 14 (2019), 105-111.
- E. Karaman, Nonsmooth set variational inequality problems and optimality criteria for set optimization, Miskolc. Math. Notes., 21(1) (2020), 229-240.
- E. Karaman, M. Soyertem, ˙I.Atasever G¨uvenc¸, Optimality conditions in set-valued optimization problem with respect to a partial order relation via directional derivative, Taiwan. J. Math., 24(3) (2020), 709-722.
- E. Karaman, ˙I. Atasever G¨uvenc¸, M. Soyertem, D.Tozkan, M. K¨uc¸¨uk, Y. K¨uc¸¨uk, , A vectorization for nonconvex set- valued optimization, Turk. J. Math., 42 (2018), 1815-1832.
- E. Karaman, M. Soyertem, ˙I. Atasever G¨uvenc¸, D. Tozkan, M. K¨uc¸¨uk, Y. K¨uc¸¨uk, Partial order relations on family of sets and scalarizations for set optimization, Positivity, 22(3) (2018), 3783-802.
- E. Karaman, ˙I. Atasever G¨uvenc¸, M. Soyertem, Optimality conditions in set-valued optimization problems with respect to a partial order relation by using subdifferentials, Optimization, 70(3) (2021) 613-630.
- Khushboo, C. S. Lalitha, Scalarizations for a set optimization problem using generalized oriented distance function, Positivity, 23(5) (2019), 1195-1213.
- D. Kuroiwa, The natural criteria in set-valued optimization, RIMS Kokyuroku, 1031(2) (1998), 85-90.
- D. Kuroiwa, On set-valued optimization, Nonlinear. Anal-Theor., 47(2) (2001), 1395-1400.
- D. Kuroiwa, Existence theorems of set optimization with set-valued maps, J. Inf. Optim. Sci., 24(1) (2003), 73-84.
- D. Kuroiwa, T. Tanaka, T. X. D. Ha, On cone convexity of set-valued maps, Nonlinear. Anal-Theor., 30(3) (1997), 1487- 1496.
- D. Pallaschke, R. Urba´nski, Pairs of Compact Convex Sets, Kluwer Academic Publishers, Dordrecht, (2002).
- M. Pilecka, Optimality conditions in set-valued programming using the set criterion, Thecnical University of Freiberg, 2014 (2014).
- R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, Cambridge, 1993.
- Y. D. Xu, S. J. Li, A new nonlinear scalarization function and applications, Optimization, 65(1) (2016), 207-231.

There are 23 citations in total.

Primary Language | English |
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Subjects | Mathematical Sciences |

Journal Section | Articles |

Authors | |

Publication Date | September 30, 2021 |

Submission Date | June 24, 2021 |

Acceptance Date | August 24, 2021 |

Published in Issue | Year 2021 Volume: 4 Issue: 3 |

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