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Autor
Hoang Nguyen Le (Department of Optimization and System Theory, University of Science of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam), Khanh Phan Quoc (Department of Mathematics, International University, Vietnam National University, Linh Trung, Thu Duc, Hochiminh City, Vietnam; Federation University, Ballarat, Victoria 3350, Australia)
Tytuł
Calculus and Applications of Studniarski's Derivatives to Sensitivity and Implicit Function Theorems
Źródło
Control and Cybernetics, 2014, vol. 43, nr 1, s. 33-57, bibliogr. s. 56-57
Słowa kluczowe
Analiza wrażliwości, Teoria optymalizacji
Sensitivity analysis, Optimization theory
Uwagi
summ.
Abstrakt
We first discuss basic calculus rules for Studniarski's derivatives. Then, we apply these derivatives to sensitivity analysis of solutions to inclusions and to computing the derivative of implicit multifunctions. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej w Warszawie
Pełny tekst
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Bibliografia
Pokaż
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  2. AUBIN, J.-P. (1981) Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions. In : Nachbin, L. (ed.) Advances in Mathematics, Supplementary studies. Acad. Press, 7A, 160-232.
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  4. DIEM, H.T.H., KHANH, P.Q. and TUNG, L.T. (2013) On higher-order sensitivity analysis in nonsmooth vector optimization. J. Optim. Theory Appl., DOI 10.1007/s10957-013-0424-3, OnlineFirst.
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  7. JIM´E NEZ, B. and NOVO, V. (2008) Higher-order optimality conditions for strict local minima. Ann. Oper. Res., 157 (1), 183-192.
  8. LI, S.J., SUN, X.K. and ZHU, S.K. (2012) Higher-order optimality conditions for strict minimality in set-valued optimization. J. Nonlinear Convex Anal., 13 (2), 281-291.
  9. LUU, D.V. (2008) Higher-order necessary and sufficient conditions for strict local Pareto minima in terms of Studniarski's derivatives. Optimization, 57 (4), 593-605.
  10. PENOT, J.-P. (1983) Compact nets, filters and relation. J. Math. Anal. Appl., 93 (2), 400-417.
  11. STUDNIARSKI, M. (1986) Necessary and sufficient conditions for isolated local minima of nonsmooth functions. SIAM J. Control Optim., 24 (5), 1044-1049.
  12. SUN, X.K. and LI, S.J. (2011) Lower Studniarski derivative of the perturbation map in parametrized vector optimization. Optim. Lett., 5 (4), 601-614.
  13. SUN, X.K. and LI, S.J. (2012) Weak lower Studniarski derivative in set-valued optimization. Pacific J. Optim., 8 (2), 307-320.
  14. TAA, A. (1998) Set-valued derivatives of multifunctions and optimality conditions. Num. Funct. Anal. Optim., 19 (1), 121-140.
  15. TANINO, T. (1988) Sensitivity analysis in multiobjective optimization. J. Optim. Theory Appl., 56 (3), 479-499.
Cytowane przez
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ISSN
0324-8569
Język
eng
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