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Volumn 18, Issue 2, 2010, Pages 205-231

On properties of different notions of centers for convex cones

Author keywords

Ball generated cone; Central axis; Convex cone; Geometry of Banach spaces; Revolution cone; Sharpness coefficient; Solidity coefficient

Indexed keywords


EID: 77952430891     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-009-0131-2     Document Type: Article
Times cited : (30)

References (26)
  • 4
    • 60449089893 scopus 로고    scopus 로고
    • A geometric analysis of Renegars condition number, and its interplay with conic curvature
    • Belloni, A., Freund, R. M.: A geometric analysis of Renegars condition number, and its interplay with conic curvature. Math. Program. 119, 95-107 (2009).
    • (2009) Math. Program. , vol.119 , pp. 95-107
    • Belloni, A.1    Freund, R.M.2
  • 6
    • 1642386955 scopus 로고    scopus 로고
    • Differentiability of cone-monotone functions on separable Banach space
    • Borwein, J. M., Burke, J. V., Lewis, A. S.: Differentiability of cone-monotone functions on separable Banach space. Proc. Am. Math. Soc. 132, 1067-1076 (2004).
    • (2004) Proc. Am. Math. Soc. , vol.132 , pp. 1067-1076
    • Borwein, J.M.1    Burke, J.V.2    Lewis, A.S.3
  • 9
    • 51249189698 scopus 로고
    • Banach spaces which can be given an equivalent uniformly convex norm
    • Enflo, P.: Banach spaces which can be given an equivalent uniformly convex norm. Israel J. Math. 13, 281-288 (1972).
    • (1972) Israel J. Math. , vol.13 , pp. 281-288
    • Enflo, P.1
  • 10
    • 0036353324 scopus 로고    scopus 로고
    • A new condition measure, preconditioners, and relations between different measures of conditioning for conic linear systems
    • Epelman, M., Freund, R. M.: A new condition measure, preconditioners, and relations between different measures of conditioning for conic linear systems. SIAM J. Optim. 12, 627-655 (2002).
    • (2002) SIAM J. Optim. , vol.12 , pp. 627-655
    • Epelman, M.1    Freund, R.M.2
  • 11
    • 0242679721 scopus 로고    scopus 로고
    • On the primal-dual geometry of level sets in linear and conic optimization
    • Freund, R. M.: On the primal-dual geometry of level sets in linear and conic optimization. SIAM J. Optim. 13, 1004-1013 (2003).
    • (2003) SIAM J. Optim. , vol.13 , pp. 1004-1013
    • Freund, R.M.1
  • 12
    • 0033261317 scopus 로고    scopus 로고
    • Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm
    • Freund, R. M., Vera, J. R.: Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm. SIAM J. Optim 10, 155-176 (1999).
    • (1999) SIAM J. Optim , vol.10 , pp. 155-176
    • Freund, R.M.1    Vera, J.R.2
  • 13
    • 0019049551 scopus 로고
    • The relaxation method for solving systems of linear inequalities
    • Goffin, J. L.: The relaxation method for solving systems of linear inequalities. Math. Oper. Res. 5, 388-414 (1980).
    • (1980) Math. Oper. Res. , vol.5 , pp. 388-414
    • Goffin, J.L.1
  • 14
    • 0028466655 scopus 로고
    • Remarks on the angle property and solid cones
    • Han, Z. Q.: Remarks on the angle property and solid cones. J. Optim. Theory Appl. 82, 149-157 (1994).
    • (1994) J. Optim. Theory Appl. , vol.82 , pp. 149-157
    • Han, Z.Q.1
  • 17
    • 33645699341 scopus 로고    scopus 로고
    • Axiomatization of the index of pointedness for closed convex cones
    • Iusem, A., Seeger, A.: Axiomatization of the index of pointedness for closed convex cones. Comput. Appl. Math. 24, 245-283 (2005).
    • (2005) Comput. Appl. Math. , vol.24 , pp. 245-283
    • Iusem, A.1    Seeger, A.2
  • 18
    • 65249090727 scopus 로고    scopus 로고
    • Searching for critical angles in a convex cone
    • Iusem, A., Seeger, A.: Searching for critical angles in a convex cone. Math. Program. 120, 3-25 (2009).
    • (2009) Math. Program. , vol.120 , pp. 3-25
    • Iusem, A.1    Seeger, A.2
  • 19
    • 34548814994 scopus 로고    scopus 로고
    • Normality and modulability indices
    • Iusem, A., Seeger, A.: Normality and modulability indices. Part I: convex cones in normed spaces. J. Math. Anal. Appl. 338, 365-391 (2008).
    • (2008) J. Math. Anal. Appl. , vol.338 , pp. 365-391
    • Iusem, A.1    Seeger, A.2
  • 20
    • 77952429079 scopus 로고    scopus 로고
    • Distances between closed convex cones: Old and new results
    • in press
    • Iusem, A., Seeger, A.: Distances between closed convex cones: old and new results. J. Convex Anal. 17 (2010, in press).
    • (2010) J. Convex Anal. , vol.17
    • Iusem, A.1    Seeger, A.2
  • 24
    • 84907062399 scopus 로고
    • Probability of error for optimal codes in a Gaussian channel
    • Shannon, C.: Probability of error for optimal codes in a Gaussian channel. Bell Syst. Tech. J. 38, 611-656 (1959).
    • (1959) Bell Syst. Tech. J. , vol.38 , pp. 611-656
    • Shannon, C.1
  • 25
    • 84966216030 scopus 로고
    • Continuity of some convex-cone-valued mappings
    • Walkup, D. W., Wets, R. J.-B.: Continuity of some convex-cone-valued mappings. Proc. Am. Math. Soc. 18, 229-235 (1967).
    • (1967) Proc. Am. Math. Soc. , vol.18 , pp. 229-235
    • Walkup, D.W.1    Wets, R.J.-B.2
  • 26
    • 0026370173 scopus 로고
    • Bases of convex cones and Borwein's proper efficiency
    • Zhuang, D. M.: Bases of convex cones and Borwein's proper efficiency. J. Optim. Theory Appl. 71, 613-620 (1991).
    • (1991) J. Optim. Theory Appl. , vol.71 , pp. 613-620
    • Zhuang, D.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.