메뉴 건너뛰기




Volumn 14, Issue 2, 2006, Pages 187-206

About regularity of collections of sets

Author keywords

Asplund space; Extremality; Normal cone; Optimality; Rugularity; Set valued mapping; Stationarity; Variational analysis

Indexed keywords


EID: 33744936851     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-006-0014-8     Document Type: Article
Times cited : (80)

References (32)
  • 2
    • 26444559124 scopus 로고    scopus 로고
    • Strong chip, normality, and linear regularity of convex sets
    • Bakan, A., Deutsch, F., Li, W.: Strong chip, normality, and linear regularity of convex sets, Trans. Amer. Math. Soc. 357(10), 3831-3863 (2005)
    • (2005) Trans. Amer. Math. Soc. , vol.357 , Issue.10 , pp. 3831-3863
    • Bakan, A.1    Deutsch, F.2    Li, W.3
  • 3
    • 0001030731 scopus 로고    scopus 로고
    • Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization
    • Bauschke, H.H., Borwein, J.M., Li, W.: Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization, Math. Program., Ser. A 86(1), 135-160 (1999)
    • (1999) Math. Program., Ser. A , vol.86 , Issue.1 , pp. 135-160
    • Bauschke, H.H.1    Borwein, J.M.2    Li, W.3
  • 4
    • 85174220840 scopus 로고    scopus 로고
    • Bounded linear regularity, strong CHIP, and CHIP are distinct properties
    • Bauschke, H.H., Borwein, J.M., Tseng, P.: Bounded linear regularity, strong CHIP, and CHIP are distinct properties, J. Convex Anal. 7(2), 395-412 (2000)
    • (2000) J. Convex Anal. , vol.7 , Issue.2 , pp. 395-412
    • Bauschke, H.H.1    Borwein, J.M.2    Tseng, P.3
  • 5
    • 0002149565 scopus 로고    scopus 로고
    • A nonconvex separation property in Banach spaces
    • Borwein, J.M., Jofré, A.: A nonconvex separation property in Banach spaces, Math. Meth. Oper. Res. 48, 169-179 (1998)
    • (1998) Math. Meth. Oper. Res. , vol.48 , pp. 169-179
    • Borwein, J.M.1    Jofré, A.2
  • 6
    • 0036924551 scopus 로고    scopus 로고
    • Weak sharp minima revisited. I. Basic theory
    • Well-posedness in optimization and related topics (Warsaw, 2001)
    • Burke, J.V., Deng, S.: Weak sharp minima revisited. I. Basic theory, Control Cybernet. 31(3), 439-469 (2002). Well-posedness in optimization and related topics (Warsaw, 2001)
    • (2002) Control Cybernet. , vol.31 , Issue.3 , pp. 439-469
    • Burke, J.V.1    Deng, S.2
  • 7
    • 27244451918 scopus 로고    scopus 로고
    • Weak sharp minima revisited. II. Application to linear regularity and error bounds
    • Burke, J.V., Deng, S.: Weak sharp minima revisited. II. Application to linear regularity and error bounds, Math. Program., Ser. B 104(2-3), 235-261. (2005)
    • (2005) Math. Program., Ser. B , vol.104 , Issue.2-3 , pp. 235-261
    • Burke, J.V.1    Deng, S.2
  • 8
    • 0027656872 scopus 로고
    • Weak sharp minima in mathematical programming
    • Burke, J.V., Ferris, M.C.: Weak sharp minima in mathematical programming, SIAM J. Control Optim. 31(5), 1340-1359 (1993)
    • (1993) SIAM J. Control Optim. , vol.31 , Issue.5 , pp. 1340-1359
    • Burke, J.V.1    Ferris, M.C.2
  • 11
    • 0034361329 scopus 로고    scopus 로고
    • Metric regularity and subdifferential calculus
    • Ioffe, A.D.: Metric regularity and subdifferential calculus, Russian Math. Surveys 55, 501-558 (2000)
    • (2000) Russian Math. Surveys , vol.55 , pp. 501-558
    • Ioffe, A.D.1
  • 13
    • 0010814679 scopus 로고    scopus 로고
    • On calculus of strict ε-semidifferentials
    • In Russian
    • Kruger, A.Y.: On calculus of strict ε-semidifferentials, Dokl. Akad. Nauk Belarusi 40(4), 34-39 (1996). In Russian
    • (1996) Dokl. Akad. Nauk Belarusi , vol.40 , Issue.4 , pp. 34-39
    • Kruger, A.Y.1
  • 14
    • 0010808808 scopus 로고    scopus 로고
    • On extremality of set systems
    • In Russian
    • Kruger, A.Y.: On extremality of set systems, Dokl. Nats. Akad. Nauk Belarusi 42(1), 24-28 (1998). In Russian
    • (1998) Dokl. Nats. Akad. Nauk Belarusi , vol.42 , Issue.1 , pp. 24-28
    • Kruger, A.Y.1
  • 15
    • 84864282115 scopus 로고    scopus 로고
    • Strict (ε, δ)-semidifferentials and extremality of sets and functions
    • In Russian
    • Kruger, A.Y.: Strict (ε, δ)-semidifferentials and extremality of sets and functions, Dokl. Nats. Akad. Nauk Belarusi 44(4), 21-24 (2000). In Russian
    • (2000) Dokl. Nats. Akad. Nauk Belarusi , vol.44 , Issue.4 , pp. 21-24
    • Kruger, A.Y.1
  • 16
    • 0036623413 scopus 로고    scopus 로고
    • Strict (ε, δ)-semidifferentials and extremality conditions
    • Kruger, A. Y.: Strict (ε, δ)-semidifferentials and extremality conditions, Optimization 51, 539-554 (2002).
    • (2002) Optimization , vol.51 , pp. 539-554
    • Kruger, A.Y.1
  • 17
    • 2542529060 scopus 로고    scopus 로고
    • On Fréchet subdifferentials
    • Optimization and related topics, 3
    • Kruger, A.Y.: On Fréchet subdifferentials, J. Math. Sci. (N.Y.) 116(3), 3325-3358 (2003). Optimization and related topics, 3
    • (2003) J. Math. Sci. (N.Y.) , vol.116 , Issue.3 , pp. 3325-3358
    • Kruger, A.Y.1
  • 18
    • 2542576238 scopus 로고    scopus 로고
    • Weak stationarity: Eliminating the gap between necessary and sufficient conditions
    • Kruger, A.Y.: Weak stationarity: Eliminating the gap between necessary and sufficient conditions, Optimization 53, 147-164 (2004)
    • (2004) Optimization , vol.53 , pp. 147-164
    • Kruger, A.Y.1
  • 19
    • 33744931869 scopus 로고    scopus 로고
    • Stationarity and regularity of set systems
    • Kruger, A.Y.: Stationarity and regularity of set systems, Pac. J. Optim. 1(1), 101-126 (2005)
    • (2005) Pac. J. Optim. , vol.1 , Issue.1 , pp. 101-126
    • Kruger, A.Y.1
  • 20
    • 33744902574 scopus 로고    scopus 로고
    • Stationarity and regularity of real-valued functions
    • To appear
    • Kruger, A.Y.: Stationarity and regularity of real-valued functions, Appl. Comput. Math. (2006). To appear
    • (2006) Appl. Comput. Math.
    • Kruger, A.Y.1
  • 21
    • 0000259921 scopus 로고
    • Extremal points and the Euler equation in nonsmooth optimization
    • In Russian
    • Kruger, A.Y., Mordukhovich, B.S.: Extremal points and the Euler equation in nonsmooth optimization, Dokl. Akad. Nauk BSSR 24(8), 684-687 (1980). In Russian
    • (1980) Dokl. Akad. Nauk BSSR , vol.24 , Issue.8 , pp. 684-687
    • Kruger, A.Y.1    Mordukhovich, B.S.2
  • 22
    • 0000686326 scopus 로고    scopus 로고
    • The extremal principle and its applications to optimization and economics
    • Rubinov, A. Glover, B. (eds.) Kluwer, Dordrecht
    • Mordukhovich, B.S.: The extremal principle and its applications to optimization and economics. In: Rubinov, A. Glover, B. (eds.) Optimization and Related Topics, Applied Optimization, vol. 47, pp. 343-369. Kluwer, Dordrecht (2001)
    • (2001) Optimization and Related Topics, Applied Optimization , vol.47 , pp. 343-369
    • Mordukhovich, B.S.1
  • 24
    • 0001657279 scopus 로고    scopus 로고
    • Extremal characterizations of Asplund spaces
    • Mordukhovich, B.S., Shao, Y.: Extremal characterizations of Asplund spaces, Proc. Amer. Math. Soc. 124, 197-205 (1996)
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 197-205
    • Mordukhovich, B.S.1    Shao, Y.2
  • 25
    • 0001004205 scopus 로고
    • Differential characterizations of covering, metric regularity, and Lipschitzian properties of multifunctions between Banach spaces
    • Mordukhovich, B.S., Shao, Y.H.: Differential characterizations of covering, metric regularity, and Lipschitzian properties of multifunctions between Banach spaces, Nonlinear Anal. 25(12), 1401-1424 (1995)
    • (1995) Nonlinear Anal. , vol.25 , Issue.12 , pp. 1401-1424
    • Mordukhovich, B.S.1    Shao, Y.H.2
  • 26
    • 21044441963 scopus 로고    scopus 로고
    • Regularities and their relations to error bounds
    • Ng, K.F., Yang, W.H.: Regularities and their relations to error bounds, Math. Program., Ser. A 99, 521-538 (2004)
    • (2004) Math. Program., Ser. A , vol.99 , pp. 521-538
    • Ng, K.F.1    Yang, W.H.2
  • 27
    • 0042283592 scopus 로고    scopus 로고
    • Metric inequality, subdifferential calculus and applications
    • Ngai, H.V., Théra, M.: Metric inequality, subdifferential calculus and applications, Set-Valued Anal. 9, 187-216 (2001)
    • (2001) Set-valued Anal. , vol.9 , pp. 187-216
    • Ngai, H.V.1    Théra, M.2
  • 28
    • 0003323056 scopus 로고
    • Convex functions, monotone operators and differentiability, 2nd edition
    • Springer, Berlin Heidelberg New York
    • Phelps, R.R.: Convex Functions, Monotone Operators and Differentiability, 2nd edition. Lecture Notes in Mathematics, vol. 1364, Springer, Berlin Heidelberg New York (1993)
    • (1993) Lecture Notes in Mathematics , vol.1364
    • Phelps, R.R.1
  • 29
    • 85049776636 scopus 로고
    • Optimization Software Inc. Publications Division, New York. Translated from Russian
    • Polyak, B.T.: Introduction to optimization. Optimization Software Inc. Publications Division, New York (1987). Translated from Russian
    • (1987) Introduction to Optimization
    • Polyak, B.T.1
  • 30
    • 0016952838 scopus 로고
    • Regularity and stability for convex multivalued functions
    • Robinson, S.M.: Regularity and stability for convex multivalued functions, Math. Oper. Res. 1(2), 130-143 (1976)
    • (1976) Math. Oper. Res. , vol.1 , Issue.2 , pp. 130-143
    • Robinson, S.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.