메뉴 건너뛰기




Volumn 55, Issue 7-8, 2003, Pages 845-858

Fenchel duality in infinite-dimensional setting and its applications

Author keywords

Convex optimization; Fenchel duality; Polyhedron; The strong conical hull intersection property

Indexed keywords

FUNCTIONS; SET THEORY; THEOREM PROVING; TOPOLOGY; VECTORS;

EID: 0242365790     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2003.07.008     Document Type: Article
Times cited : (25)

References (19)
  • 1
    • 0013468395 scopus 로고
    • Duality for the sum of convex functions in general Banach spaces
    • J. Barroso. Amsterdam: North-Holland
    • Attouch H., Brézis H. Duality for the sum of convex functions in general Banach spaces. Barroso J. Aspect of Mathematics and its Applications. 1986;125-133 North-Holland, Amsterdam.
    • (1986) Aspect of Mathematics and Its Applications , pp. 125-133
    • Attouch, H.1    Brézis, H.2
  • 3
    • 0033245924 scopus 로고    scopus 로고
    • Proof of a conjecture by Deutsch, LI, and Swettis on duality of optimization problems
    • Bauschke H.H. Proof of a conjecture by Deutsch, LI, and Swettis on duality of optimization problems. J. Optim. Theory Appl. 102:1999;697-703.
    • (1999) J. Optim. Theory Appl. , vol.102 , pp. 697-703
    • Bauschke, H.H.1
  • 4
    • 0026867929 scopus 로고
    • Partially finite convex programming, part I: Quasi relative interiors and duality
    • Borwein J.M., Lewis A.S. Partially finite convex programming, part I. quasi relative interiors and duality Math. Programming. 57:1992;15-48.
    • (1992) Math. Programming , vol.57 , pp. 15-48
    • Borwein, J.M.1    Lewis, A.S.2
  • 5
    • 0033245917 scopus 로고    scopus 로고
    • Fenchel duality and the strong conical hull intersection property
    • Deutsch F., Li W., Swettis J. Fenchel duality and the strong conical hull intersection property. J. Optim. Theory Appl. 102:1999;681-695.
    • (1999) J. Optim. Theory Appl. , vol.102 , pp. 681-695
    • Deutsch, F.1    Li, W.2    Swettis, J.3
  • 6
    • 0001669049 scopus 로고    scopus 로고
    • A dual approach to constrained interpolation from a convex subset of Hilber space
    • Deutsch F., Li W., Ward J.D. A dual approach to constrained interpolation from a convex subset of Hilber space. SIAM J. Optim. 90:1997;385-414.
    • (1997) SIAM J. Optim. , vol.90 , pp. 385-414
    • Deutsch, F.1    Li, W.2    Ward, J.D.3
  • 7
    • 0033266805 scopus 로고    scopus 로고
    • Best approximation from the intersection of a closed convex set and a polyhedron in Hilbert space, weak Slater conditions, and the strong conical hull intersection property
    • Deutsch F., Li W., Ward J.D. Best approximation from the intersection of a closed convex set and a polyhedron in Hilbert space, weak Slater conditions, and the strong conical hull intersection property. SIAM J. Optim. 10:1999;252-268.
    • (1999) SIAM J. Optim. , vol.10 , pp. 252-268
    • Deutsch, F.1    Li, W.2    Ward, J.D.3
  • 8
    • 0025462417 scopus 로고
    • A comparison of constraint qualification in infinite-dimensional convex programming
    • Gowda M.S., Teboulle M. A comparison of constraint qualification in infinite-dimensional convex programming. SIAM J. Control Optim. 28:1990;925-935.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 925-935
    • Gowda, M.S.1    Teboulle, M.2
  • 10
    • 0025533626 scopus 로고
    • Duality and infinite dimensional optimization
    • Jeyakumar V. Duality and infinite dimensional optimization. Nonlinear Anal. TMA. 15:1990;1111-1122.
    • (1990) Nonlinear Anal. TMA , vol.15 , pp. 1111-1122
    • Jeyakumar, V.1
  • 11
    • 0026867587 scopus 로고
    • Generalization of Slater's constraint qualification for infinite convex programs
    • Jeyakumar V., Wolkowicz H. Generalization of Slater's constraint qualification for infinite convex programs. Math. Programming. 57B:1992;85-101.
    • (1992) Math. Programming , vol.57 B , pp. 85-101
    • Jeyakumar, V.1    Wolkowicz, H.2
  • 13
    • 0002793794 scopus 로고
    • Level sets and continuity of conjugate convex functions
    • Rockafellar R.T. Level sets and continuity of conjugate convex functions. Trans. Amer. Math. Soc. 123:1966;46-63.
    • (1966) Trans. Amer. Math. Soc. , vol.123 , pp. 46-63
    • Rockafellar, R.T.1
  • 14
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton University Press
    • Rockafellar R.T. Convex Analysis. 1970;Princeton University Press, Princeton, NJ.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 15
    • 0003350183 scopus 로고
    • Conjugate Duality and Optimization, CBMS-NSF Regional Conference
    • SIAM, Philadephia, PA
    • R.T. Rockafellar, Conjugate Duality and Optimization, CBMS-NSF Regional Conference in Applied Mathematics, Vol. 16, SIAM, Philadephia, PA, 1974.
    • (1974) Applied Mathematics , vol.16
    • Rockafellar, R.T.1
  • 16
    • 0011279317 scopus 로고
    • Conjugate functions and subdiffrerentials in nonnormed situations for operators with complete graphs
    • Rodrigues B., Simons S. Conjugate functions and subdiffrerentials in nonnormed situations for operators with complete graphs. Nonlinear Anal. TMA. 12:1988;1069-1078.
    • (1988) Nonlinear Anal. TMA. , vol.12 , pp. 1069-1078
    • Rodrigues, B.1    Simons, S.2
  • 17
    • 0032164745 scopus 로고    scopus 로고
    • Duality for optimization and best approximation over finite intersections
    • Singer I. Duality for optimization and best approximation over finite intersections. Numer. Func. Anal. Optim. 19(7&8):1998;903-915.
    • (1998) Numer. Func. Anal. Optim. , vol.19 , Issue.7-8 , pp. 903-915
    • Singer, I.1
  • 18
    • 4243384962 scopus 로고    scopus 로고
    • A comparison of constraint qualifications in infinite-dimensional convex programming revisited
    • Zǎlinescu C. A comparison of constraint qualifications in infinite-dimensional convex programming revisited. J. Austral. Math. Soc. Ser. B40:1999;353-378.
    • (1999) J. Austral. Math. Soc. Ser. , vol.B40 , pp. 353-378
    • Zǎlinescu, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.