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Volumn 17, Issue 1, 2009, Pages 21-39

Calculus rules for derivatives of multimaps

Author keywords

Calmness; Contingent derivative; Incident derivative; Proto differentiability; Semi differentiability; Upper Lipschitz property

Indexed keywords


EID: 73549118596     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-009-0105-4     Document Type: Article
Times cited : (31)

References (22)
  • 1
    • 0001149753 scopus 로고
    • On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems
    • Ahmaroq, T., Thibault, L.: On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems. Numer. Funct. Anal. Optim. 16, 1293-1307 (1995)
    • (1995) Numer. Funct. Anal. Optim. , vol.16 , pp. 1293-1307
    • Ahmaroq, T.1    Thibault, L.2
  • 3
    • 0038237445 scopus 로고    scopus 로고
    • On the calmness of a class of multifunctions
    • Henrion, R., Jourani, A., Outrata, J.: On the calmness of a class of multifunctions. SIAM J. Optim. 13(2), 603-618 (2002)
    • (2002) SIAM J. Optim. , vol.13 , Issue.2 , pp. 603-618
    • Henrion, R.1    Jourani, A.2    Outrata, J.3
  • 4
    • 0000149620 scopus 로고    scopus 로고
    • Subdifferentials of performance functions and calculus of set-valued mappings
    • Ioffe, A.D., Penot, J.-P.: Subdifferentials of performance functions and calculus of set-valued mappings. Serdica Math. J. 22, 359-384 (1996)
    • (1996) Serdica Math. J. , vol.22 , pp. 359-384
    • Ioffe, A.D.1    Penot, J.-P.2
  • 5
    • 34249843405 scopus 로고
    • Sensitivity analysis for nonsmooth generalized equations
    • King, A.J., Rockafellar, R.T.: Sensitivity analysis for nonsmooth generalized equations. Math. Program. 55(2), 193-212 (1992)
    • (1992) Math. Program. , vol.55 , Issue.2 , pp. 193-212
    • King, A.J.1    Rockafellar, R.T.2
  • 6
    • 0026219859 scopus 로고
    • Lipschitzian inverse functions, directional derivatives, and applications to C1,1 optimization
    • Kummer, B.: Lipschitzian inverse functions, directional derivatives, and applications to C1,1 optimization. J. Optim. Theory Appl. 70(3), 561-581 (1991)
    • (1991) J. Optim. Theory Appl. , vol.70 , Issue.3 , pp. 561-581
    • Kummer, B.1
  • 7
    • 0012226056 scopus 로고    scopus 로고
    • Metric regularity: Characterizations, nonsmooth variations and successive approximation
    • Kummer, B.: Metric regularity: characterizations, nonsmooth variations and successive approximation. Optimization 46(3), 247-281 (1999)
    • (1999) Optimization , vol.46 , Issue.3 , pp. 247-281
    • Kummer, B.1
  • 8
    • 33749514260 scopus 로고    scopus 로고
    • On proto-differentiability of generalized perturbation maps
    • Lee, G.M., Huy, N.Q.: On proto-differentiability of generalized perturbation maps. J. Math. Anal. Appl. 324, 1297-1309 (2006)
    • (2006) J. Math. Anal. Appl. , vol.324 , pp. 1297-1309
    • Lee, G.M.1    Huy, N.Q.2
  • 9
    • 0008693608 scopus 로고    scopus 로고
    • Implicit multifunction theorems for the sensitivity of analysis of variational conditions
    • Levy, A.B.: Implicit multifunction theorems for the sensitivity of analysis of variational conditions. Math. Program. 74, 333-350 (1996)
    • (1996) Math. Program. , vol.74 , pp. 333-350
    • Levy, A.B.1
  • 10
    • 0008714646 scopus 로고    scopus 로고
    • Nonsingularity conditions for multifunctions
    • Levy, A.B.: Nonsingularity conditions for multifunctions. Set-Valued Anal. 7(1), 89-99 (1999)
    • (1999) Set-Valued Anal. , vol.7 , Issue.1 , pp. 89-99
    • Levy, A.B.1
  • 11
    • 0035261813 scopus 로고    scopus 로고
    • Lipschitzian multifunctions and a Lipschitzian inverse mapping theorem
    • Levy, A.B.: Lipschitzian multifunctions and a Lipschitzian inverse mapping theorem. Math. Oper. Res. 26(1), 105-118 (2001)
    • (2001) Math. Oper. Res. , vol.26 , Issue.1 , pp. 105-118
    • Levy, A.B.1
  • 13
    • 0002399446 scopus 로고
    • Compact nets, filters and relations
    • Penot, J.-P.: Compact nets, filters and relations. J. Math. Anal. Appl. 93(2), 400-417 (1983)
    • (1983) J. Math. Anal. Appl. , vol.93 , Issue.2 , pp. 400-417
    • Penot, J.-P.1
  • 15
    • 0021466350 scopus 로고
    • Differentiability of relations and differential stability of perturbed optimization problems
    • Erratum, idem, 26(4), 997 (1988)
    • Penot, J.-P.: Differentiability of relations and differential stability of perturbed optimization problems. SIAM J. Control Optim. 22(4), 529- 551 (1984). Erratum, idem, 26(4), 997 (1988)
    • (1984) SIAM J. Control Optim. , vol.22 , Issue.4 , pp. 529-551
    • Penot, J.-P.1
  • 16
    • 1642500111 scopus 로고    scopus 로고
    • Continuity of usual operations and variational convergences
    • Penot, J.-P., Zalinescu, C.: Continuity of usual operations and variational convergences. Set-Valued Anal. 11(3), 225-256 (2003)
    • (2003) Set-Valued Anal. , vol.11 , Issue.3 , pp. 225-256
    • Penot, J.-P.1    Zalinescu, C.2
  • 17
    • 0000516813 scopus 로고
    • An implicit-function theorem for a class of nonsmooth functions
    • Robinson, S.M.: An implicit-function theorem for a class of nonsmooth functions. Math. Oper. Res. 16, 292-309 (1991)
    • (1991) Math. Oper. Res. , vol.16 , pp. 292-309
    • Robinson, S.M.1
  • 18
    • 0001519757 scopus 로고
    • Proto-differentiability of set-valued mappings and its applications in optimization
    • H. Attouch (Ed.), Paris: Gauthier-Villars
    • Rockafellar, R.T.: Proto-differentiability of set-valued mappings and its applications in optimization. In: Attouch, H., et al. (eds.) Analyse Non Linèaire, pp. 449-482. Gauthier-Villars, Paris (1989)
    • (1989) Analyse Non LinèAire , pp. 449-482
    • Rockafellar, R.T.1
  • 20
    • 0026206256 scopus 로고
    • Contingent derivative of the perturbation map in multiobjective optimization
    • Shi, S.S.: Contingent derivative of the perturbation map in multiobjective optimization. J. Optim. Theory Appl. 70(2), 385-396 (1991)
    • (1991) J. Optim. Theory Appl. , vol.70 , Issue.2 , pp. 385-396
    • Shi, S.S.1
  • 21
    • 84967712812 scopus 로고
    • Tangent cones and quasi-interior tangent cones to multifunctions
    • Thibault, L., Tangent cones and quasi-interior tangent cones to multifunctions. Trans. Amer. Math. Soc. 277, 601-621 (1983)
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 601-621
    • Thibault, L.1
  • 22
    • 84967708668 scopus 로고
    • Generalized gradients and applications
    • Clarke, F.H.: Generalized gradients and applications. Trans. Amer. Math. Soc. 205, 247-262 (1975)
    • (1975) Trans. Amer. Math. Soc. , vol.205 , pp. 247-262
    • Clarke, F.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.