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Volumn 17, Issue 2, 2006, Pages 353-371

Calmness and error bounds for convex constraint systems

Author keywords

Calmness; Convex systems; Error bounds; Local linear regularity; Set valued mapping

Indexed keywords

ERROR ANALYSIS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

EID: 34249100220     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623403430361     Document Type: Article
Times cited : (20)

References (29)
  • 2
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • H. H. BAUSCHKE AND J. M. BORWEIN, On projection algorithms for solving convex feasibility problems, SIAM Rev., 38 (1996), pp. 367-426.
    • (1996) SIAM Rev , vol.38 , pp. 367-426
    • BAUSCHKE, H.H.1    BORWEIN, J.M.2
  • 3
    • 0001030731 scopus 로고    scopus 로고
    • Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization
    • H. H. BAUSCHKE, J. M. BORWEIN, AND W. LI, Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization, Math. Program. Ser. A, 86 (1999), pp. 135-160.
    • (1999) Math. Program. Ser. A , vol.86 , pp. 135-160
    • BAUSCHKE, H.H.1    BORWEIN, J.M.2    LI, W.3
  • 4
    • 0000895022 scopus 로고
    • Tangential approximations
    • J. M. BORWEIN AND H. M. STROJWAS, Tangential approximations, Nonlinear Anal., 9 (1985), pp. 1347-1366.
    • (1985) Nonlinear Anal , vol.9 , pp. 1347-1366
    • BORWEIN, J.M.1    STROJWAS, H.M.2
  • 5
    • 0026118632 scopus 로고
    • Calmness and exact penalization
    • J. V. BURKE, Calmness and exact penalization, SIAM J. Control Optim., 29 (1991), pp. 493-497.
    • (1991) SIAM J. Control Optim , vol.29 , pp. 493-497
    • BURKE, J.V.1
  • 6
    • 27844527163 scopus 로고
    • On the Clarke subdifferential of the distance function of a closed set
    • J. BURKE, M. C. FERRIS, AND M. QIAN, On the Clarke subdifferential of the distance function of a closed set, J. Math. Anal. Appl., 166 (1992), pp. 199-213.
    • (1992) J. Math. Anal. Appl , vol.166 , pp. 199-213
    • BURKE, J.1    FERRIS, M.C.2    QIAN, M.3
  • 8
    • 3943050689 scopus 로고    scopus 로고
    • Regularity and conditioning of solution mappings in variational analysis
    • A. L. DONTCHEV AND R. T. ROCKAFELLAR, Regularity and conditioning of solution mappings in variational analysis, Set-Valued Anal., 12 (2004), pp. 79-109.
    • (2004) Set-Valued Anal , vol.12 , pp. 79-109
    • DONTCHEV, A.L.1    ROCKAFELLAR, R.T.2
  • 9
    • 0001612328 scopus 로고    scopus 로고
    • A subdifferential condition for calmness of multifunction
    • R. HENRION AND J. OUTRATA, A subdifferential condition for calmness of multifunction, J. Math. Anal. Appl., 258 (2001), pp. 110-130.
    • (2001) J. Math. Anal. Appl , vol.258 , pp. 110-130
    • HENRION, R.1    OUTRATA, J.2
  • 10
    • 0038237446 scopus 로고    scopus 로고
    • Subdifferential conditions for calmness of convex constraints
    • R. HENRION AND A. JOURANI, Subdifferential conditions for calmness of convex constraints, SIAM J. Optim., 13 (2002), pp. 520-534.
    • (2002) SIAM J. Optim , vol.13 , pp. 520-534
    • HENRION, R.1    JOURANI, A.2
  • 11
    • 0038237445 scopus 로고    scopus 로고
    • On the calmness of a class of multifunctions
    • R. HENRION, A. JOURANI, AND J. OUTRATA, On the calmness of a class of multifunctions, SIAM J. Optim., 13 (2002), pp. 603-618.
    • (2002) SIAM J. Optim , vol.13 , pp. 603-618
    • HENRION, R.1    JOURANI, A.2    OUTRATA, J.3
  • 13
    • 84867959059 scopus 로고
    • Regular points of Lipschitz functions
    • A. IOFFE, Regular points of Lipschitz functions, Trans. Amer. Math. Soc., 251 (1975), pp. 61-69.
    • (1975) Trans. Amer. Math. Soc , vol.251 , pp. 61-69
    • IOFFE, A.1
  • 14
    • 0018441517 scopus 로고
    • Necessary and sufficient conditions for a local minimum, I: A reduction theorem and first order conditions
    • A. D. IOFFE, Necessary and sufficient conditions for a local minimum, I: A reduction theorem and first order conditions, SIAM J. Control Optim., 17 (1979), pp. 245-250.
    • (1979) SIAM J. Control Optim , vol.17 , pp. 245-250
    • IOFFE, A.D.1
  • 15
    • 0034361329 scopus 로고    scopus 로고
    • Metric regularity and subdifferential calculus
    • A. D. IOFFE, Metric regularity and subdifferential calculus, Russian Math. Surveys, 55 (2000), pp. 501-558.
    • (2000) Russian Math. Surveys , vol.55 , pp. 501-558
    • IOFFE, A.D.1
  • 16
    • 84963062942 scopus 로고
    • The duality of pairs of wedges
    • G. J. O. JAMESON, The duality of pairs of wedges, Proc. London Math. Soc., 249 (1972), pp. 531-547.
    • (1972) Proc. London Math. Soc , vol.249 , pp. 531-547
    • JAMESON, G.J.O.1
  • 17
    • 0038328485 scopus 로고
    • Intersection formulae and the marginal function in Danach spaces
    • A. JOURANI, Intersection formulae and the marginal function in Danach spaces, J. Math. Anal. Appl., 192 (1995), pp. 867-891.
    • (1995) J. Math. Anal. Appl , vol.192 , pp. 867-891
    • JOURANI, A.1
  • 18
    • 0033102269 scopus 로고    scopus 로고
    • Coderivatives of multivalued mappings, locally compact cones and metric regularity
    • A. JOURANI AND L. THIBAULT, Coderivatives of multivalued mappings, locally compact cones and metric regularity, Nonlinear Anal., 35 (1999), pp. 925-945.
    • (1999) Nonlinear Anal , vol.35 , pp. 925-945
    • JOURANI, A.1    THIBAULT, L.2
  • 19
    • 0038473931 scopus 로고    scopus 로고
    • Constrained minima and Lipschitzian penalties in metric spaces
    • D. KLATTE AND B. KUMMER, Constrained minima and Lipschitzian penalties in metric spaces, SIAM J. Optim., 13 (2002), pp. 619-633.
    • (2002) SIAM J. Optim , vol.13 , pp. 619-633
    • KLATTE, D.1    KUMMER, B.2
  • 20
    • 0002449351 scopus 로고    scopus 로고
    • Error bounds for convex inequality systems
    • J.-P. Crouzex, J.-E. Martinez-Legaz, and M. Volle, eds, Kluwer Academic, Dordrecht, The Netherlands
    • A. S. LEWIS AND J. S. PANG, Error bounds for convex inequality systems, in Proceedings of the 5th International Symposium on Generalized Convexity, Luminy, 1996, J.-P. Crouzex, J.-E. Martinez-Legaz, and M. Volle, eds., Kluwer Academic, Dordrecht, The Netherlands, 1998, pp. 75-110.
    • (1996) Proceedings of the 5th International Symposium on Generalized Convexity, Luminy , pp. 75-110
    • LEWIS, A.S.1    PANG, J.S.2
  • 21
    • 0032072970 scopus 로고    scopus 로고
    • Global error bounds for convex multifunctions and applications
    • W. LI AND I. SINGER, Global error bounds for convex multifunctions and applications, Math. Oper. Res., 23 (1998), pp. 443-462.
    • (1998) Math. Oper. Res , vol.23 , pp. 443-462
    • LI, W.1    SINGER, I.2
  • 22
    • 0001442538 scopus 로고
    • Limits of Fréchet normals in nonsmooth analysis, in Optimization and Nonlinear Analysis
    • A. D. Ioffe et al, eds, Notes Math. Ser. 244, Longman Scientific & Technical, Harlow, UK
    • P. D. LOEWEN, Limits of Fréchet normals in nonsmooth analysis, in Optimization and Nonlinear Analysis, A. D. Ioffe et al., eds., Pitman Res. Notes Math. Ser. 244, Longman Scientific & Technical, Harlow, UK, 1992, pp. 178-188.
    • (1992) Pitman Res , pp. 178-188
    • LOEWEN, P.D.1
  • 23
    • 27244452009 scopus 로고    scopus 로고
    • Nonsmooth sequential analysis in Asplund spaces
    • B. S. MORDUKHOVICH AND Y. SHAO, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc., 348 (1996), pp. 1235-1280.
    • (1996) Trans. Amer. Math. Soc , vol.348 , pp. 1235-1280
    • MORDUKHOVICH, B.S.1    SHAO, Y.2
  • 24
    • 0000108034 scopus 로고    scopus 로고
    • Nonconvex differential calculus for infinite-dimensional multifunctions
    • B. S. MORDUKHOVICH AND Y. SHAO, Nonconvex differential calculus for infinite-dimensional multifunctions, Set-Valued Anal., 4 (1996), pp. 205-236.
    • (1996) Set-Valued Anal , vol.4 , pp. 205-236
    • MORDUKHOVICH, B.S.1    SHAO, Y.2
  • 25
    • 0030735808 scopus 로고    scopus 로고
    • Stability of set-valued mappings in infinite dimensions: Point criteria and applications
    • B. S. MORDUKHOVICH AND Y. SHAO, Stability of set-valued mappings in infinite dimensions: Point criteria and applications, SIAM J. Control Optim., 35 (1997), pp. 285-314.
    • (1997) SIAM J. Control Optim , vol.35 , pp. 285-314
    • MORDUKHOVICH, B.S.1    SHAO, Y.2
  • 26
    • 0037288592 scopus 로고    scopus 로고
    • Error bounds for abstract linear inequality systems
    • K. F. NG AND W. H. YANG, Error bounds for abstract linear inequality systems, SIAM J. Optim., 13 (2002), pp. 24-43.
    • (2002) SIAM J. Optim , vol.13 , pp. 24-43
    • NG, K.F.1    YANG, W.H.2
  • 27
    • 0016952838 scopus 로고
    • Regularity and stability for convex multivalued functions
    • S. ROBINSON, Regularity and stability for convex multivalued functions, Math. Oper. Res., 1 (1976), pp. 130-143.
    • (1976) Math. Oper. Res , vol.1 , pp. 130-143
    • ROBINSON, S.1
  • 29
    • 29144468040 scopus 로고    scopus 로고
    • Bounded linear regularity of convex sets in Banach spaces
    • W. SONG AND R. ZANG, Bounded linear regularity of convex sets in Banach spaces, Math. Program., 106 (2006), pp. 59-79.
    • (2006) Math. Program , vol.106 , pp. 59-79
    • SONG, W.1    ZANG, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.