Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

• Autorzy: Stasiak A.

Identyfikatory

DOI

10.1515/jaa-2018-0005

• Języki publikacji: EN

Abstrakty

EN

Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212-221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

Słowa kluczowe

EN

vector optimization; higher-order conditions; lower directional derivatives; upper directional derivatives; polyhedral cone

PL

optymalizacja wektorowa; warunki wyższego rzędu; górne pochodne kierunkowe; dolne pochodne kierunkowe; stożek wielościenny

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 1
• Strony: 45--54
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Stasiak A.

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., Springer, New York, 2003.
• [2] A. Göpfert, C. Tammer, H. Riahi and C. Zălinescu, Variational Methods in Partially Ordered Spaces, Springer, New York, 2003.
• [3] B. Jiménez, Strict efficiency in vector optimization, J. Math. Anal. Appl. 265 (2002), 264-284.
• [4] B. Jiménez, Strict minimality conditions in nondifferentiable multiobjective programming, J. Optim. Theory Appl. 116 (2003), no. 1, 99-116.
• [5] B. Jiménez and V. Novo, Higher-order optimality conditions for strict local minima, Ann. Oper. Res. 157 (2008), 183-192.
• [6] D. V. Luu, Higher-order necessary and sufficient conditions for strict Pareto minima in terms of Studniarski’s derivatives, Optimization 57 (2008), no. 4, 593-605.
• [7] D. V. Luu and P. T. Kien, On higher-order conditions for strict efficiency, Soochow J. Math. 33 (2007), no. 1, 17-31.
• [8] E.-D. Rahmo, A. Stasiak and M. Studniarski, Lower and upper Ginchev derivatives of vector functions and their applications to multiobjective optimization, Optim. Lett. 8 (2014), no. 2, 653-667.
• [9] E.-D. Rahmo and M. Studniarski, Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives, J. Math. Anal. Appl. 393 (2012), 212-221.
• [10] M. Studniarski, Necessary and sufficient conditions for isolated local minima of nonsmooth functions, SIAM J. Control Optim. 24 (1986), 1044-1049.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).