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2014 | 43 | nr 1 | 33--57
Tytuł artykułu

Calculus and Applications of Studniarski's Derivatives to Sensitivity and Implicit Function Theorems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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)
Rocznik
Tom
43
Numer
Strony
33--57
Opis fizyczny
Twórcy
  • Department of Optimization and System Theory, University of Science of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam
  • Department of Mathematics, International University, Vietnam National University, Linh Trung, Thu Duc, Hochiminh City, Vietnam; Federation University, Ballarat, Victoria 3350, Australia
Bibliografia
  • ANH, N.L.H., KHANH, P.Q. and TUNG, L.T. (2011) Higher-order radial derivatives and optimality conditions in nonsmooth vector optimization. Nonlinear Anal. TMA, 74(18), 7365-7379.
  • 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.
  • BEDNARCZUK, E.M. and SONG, W. (1998) Contingent epiderivative and its applications to set-valued optimization. Control Cybern., 27 (3), 375-386.
  • 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.
  • JAHN, J. and RAUH, R (1997) Contingent Epiderivatives and Set-Valued Optimization. Math. Meth. Oper. Res., 46 (2), 193-211.
  • JIM´E NEZ, B. (2003) Strict minimality conditions in nondifferentiable multiobjective programming. J. Optim. Theory Appl., 116 (1), 99-116.
  • JIM´E NEZ, B. and NOVO, V. (2008) Higher-order optimality conditions for strict local minima. Ann. Oper. Res., 157 (1), 183-192.
  • 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.
  • 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.
  • PENOT, J.-P. (1983) Compact nets, filters and relation. J. Math. Anal. Appl., 93 (2), 400-417.
  • STUDNIARSKI, M. (1986) Necessary and sufficient conditions for isolated local minima of nonsmooth functions. SIAM J. Control Optim., 24 (5), 1044-1049.
  • 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.
  • SUN, X.K. and LI, S.J. (2012) Weak lower Studniarski derivative in set-valued optimization. Pacific J. Optim., 8 (2), 307-320.
  • TAA, A. (1998) Set-valued derivatives of multifunctions and optimality conditions. Num. Funct. Anal. Optim., 19 (1), 121-140.
  • TANINO, T. (1988) Sensitivity analysis in multiobjective optimization. J. Optim. Theory Appl., 56 (3), 479-499.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171479599

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