메뉴 건너뛰기




Volumn 6, Issue 2, 1999, Pages 235-266

Graph-convex mappings and K-convex functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 22844454292     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (21)

References (43)
  • 1
    • 0003086078 scopus 로고
    • Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions
    • Ed. L. Nachbin
    • J.-P. Aubin: Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions, Advances in Mathematics, Supplementary studies, Ed. L. Nachbin (1981) 160-232.
    • (1981) Advances in Mathematics, Supplementary Studies , pp. 160-232
    • Aubin, J.-P.1
  • 4
    • 0002279147 scopus 로고
    • Multivalued convexity and optimization: A unified approach to inequality and equality constraints
    • J. M. Borwein: Multivalued convexity and optimization: A unified approach to inequality and equality constraints, Math. Programming 13 (1977) 183-199.
    • (1977) Math. Programming , vol.13 , pp. 183-199
    • Borwein, J.M.1
  • 5
    • 0002820799 scopus 로고
    • Proper efficient points for maximizations with respect to cones
    • J. M. Borwein: Proper efficient points for maximizations with respect to cones, SIAM J. Control Optim. 15 (1977) 57-63.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 57-63
    • Borwein, J.M.1
  • 6
    • 0000297125 scopus 로고
    • Continuity and differentiability properties of convex operators
    • J. M. Borwein: Continuity and differentiability properties of convex operators, Proc. London Math. Soc. 44(3) (1982) 420-444.
    • (1982) Proc. London Math. Soc. , vol.44 , Issue.3 , pp. 420-444
    • Borwein, J.M.1
  • 7
    • 84968486933 scopus 로고
    • Automatic continuity and openness of convex relations
    • J. M. Borwein: Automatic continuity and openness of convex relations, Proc. Amer. Math. Soc. 99(1) (1987) 49-55.
    • (1987) Proc. Amer. Math. Soc. , vol.99 , Issue.1 , pp. 49-55
    • Borwein, J.M.1
  • 8
    • 84968494969 scopus 로고
    • Super efficiency in vector optimization
    • J. M. Borwein: Super efficiency in vector optimization, Trans. Amer. Math. Soc. 338(1) (1993) 105-122.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , Issue.1 , pp. 105-122
    • Borwein, J.M.1
  • 10
    • 0011376467 scopus 로고
    • All convex invariant functions of Hermitian matrices
    • C. Davis: All convex invariant functions of Hermitian matrices, Archiv der Mathematik 8 (1957) 276-278.
    • (1957) Archiv der Mathematik , vol.8 , pp. 276-278
    • Davis, C.1
  • 11
    • 0002509696 scopus 로고
    • Inverse eigenvalue problems
    • S. Friedland: Inverse eigenvalue problems, Linear Algebra Appl. 17 (1977) 15-51.
    • (1977) Linear Algebra Appl. , vol.17 , pp. 15-51
    • Friedland, S.1
  • 15
    • 0000183491 scopus 로고
    • Subdifferential calculus without qualification conditions, using approximate subdifferentials: A survey
    • J.-B. Hiriart-Urruty, M. Moussaoui, A. Seeger, M. Volle: Subdifferential calculus without qualification conditions, using approximate subdifferentials: a survey, Nonlinear Analysis 24(12) (1995) 1727-1754.
    • (1995) Nonlinear Analysis , vol.24 , Issue.12 , pp. 1727-1754
    • Hiriart-Urruty, J.-B.1    Moussaoui, M.2    Seeger, A.3    Volle, M.4
  • 16
    • 21844488492 scopus 로고
    • Sensitivity analysis of all eigenvalues of a symmetric matrix
    • J.-B. Hiriart-Urruty, D. Ye: Sensitivity analysis of all eigenvalues of a symmetric matrix, Numer. Math. 70 (1995) 45-72.
    • (1995) Numer. Math. , vol.70 , pp. 45-72
    • Hiriart-Urruty, J.-B.1    Ye, D.2
  • 20
    • 25444533440 scopus 로고
    • Subdifferentials of convex mappings and composite functions
    • V. L. Levin: Subdifferentials of convex mappings and composite functions, Siberian Math. J. 13 (1972) 903-909.
    • (1972) Siberian Math. J. , vol.13 , pp. 903-909
    • Levin, V.L.1
  • 21
    • 25444486255 scopus 로고    scopus 로고
    • Von Neumann's lemma and a Chevalley-type theorem for convex functions on Cartan subspaces
    • submitted
    • A. S. Lewis: Von Neumann's lemma and a Chevalley-type theorem for convex functions on Cartan subspaces, Trans. Amer. Math. Soc., submitted.
    • Trans. Amer. Math. Soc.
    • Lewis, A.S.1
  • 22
    • 0039119760 scopus 로고
    • The convex analysis of unitarily invariant matrix functions
    • A. S. Lewis: The convex analysis of unitarily invariant matrix functions, J. Convex Analysis 2(1) (1995) 173-183.
    • (1995) J. Convex Analysis , vol.2 , Issue.1 , pp. 173-183
    • Lewis, A.S.1
  • 23
    • 0030304775 scopus 로고    scopus 로고
    • Convex analysis on the Hermitian matrices
    • A. S. Lewis: Convex analysis on the Hermitian matrices, SIAM J. Optim. 6 (1996) 164-177.
    • (1996) SIAM J. Optim. , vol.6 , pp. 164-177
    • Lewis, A.S.1
  • 24
    • 0030518228 scopus 로고    scopus 로고
    • Group invariance and convex matrix analysis
    • A. S. Lewis: Group invariance and convex matrix analysis, SIAM J. Matrix Anal. Appl. 17(4) (1996) 927-949.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.4 , pp. 927-949
    • Lewis, A.S.1
  • 26
    • 0001254208 scopus 로고
    • Metric approximations and necessary conditions for general classes of nonsmooth extremal problems
    • B. S. Mordukhovich: Metric approximations and necessary conditions for general classes of nonsmooth extremal problems, Soviet Math. Dokl. 22(2) (1980) 526-530.
    • (1980) Soviet Math. Dokl. , vol.22 , Issue.2 , pp. 526-530
    • Mordukhovich, B.S.1
  • 27
    • 0000551562 scopus 로고
    • Generalized differential calculus for nonsmooth and set-valued mappings
    • B. S. Mordukhovich: Generalized differential calculus for nonsmooth and set-valued mappings, J. Math. Anal. Appl. 183 (1994) 250-288.
    • (1994) J. Math. Anal. Appl. , vol.183 , pp. 250-288
    • Mordukhovich, B.S.1
  • 28
    • 0000108034 scopus 로고    scopus 로고
    • Nonconvex differential calculus for infinite-dimensional multifunctions
    • B. S. Mordukhovich, Y. Shao: Nonconvex differential calculus for infinite-dimensional multifunctions, Set-Valued Anal. 4(3) (1996) 205-236.
    • (1996) Set-Valued Anal. , vol.4 , Issue.3 , pp. 205-236
    • Mordukhovich, B.S.1    Shao, Y.2
  • 29
    • 0003181133 scopus 로고
    • Large-scale optimization of eigenvalues
    • M. L. Overton: Large-scale optimization of eigenvalues, SIAM J. Optim. 2(1) (1992) 88-120.
    • (1992) SIAM J. Optim. , vol.2 , Issue.1 , pp. 88-120
    • Overton, M.L.1
  • 30
    • 34250080273 scopus 로고
    • Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrix
    • K. L. Overton, R. S. Womersley: Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrix, Math. Programming 62 (1993) 321-357.
    • (1993) Math. Programming , vol.62 , pp. 321-357
    • Overton, K.L.1    Womersley, R.S.2
  • 31
    • 0034403146 scopus 로고    scopus 로고
    • Dualization of generalized equations of maximal monotone type
    • T. Pennanen: Dualization of generalized equations of maximal monotone type, to appear in SIAM J. Optim.
    • SIAM J. Optim.
    • Pennanen, T.1
  • 32
    • 25444460461 scopus 로고    scopus 로고
    • Generalized Jacobians of vector-valued convex functions
    • T. Pennanen, J. Eckstein: Generalized Jacobians of vector-valued convex functions, Rutcor Research Reports (1997) 6-97.
    • (1997) Rutcor Research Reports , pp. 6-97
    • Pennanen, T.1    Eckstein, J.2
  • 33
    • 0016952838 scopus 로고
    • Regularity and stability for convex multivalued functions
    • S. M. Robinson: Regularity and stability for convex multivalued functions, Math. Oper. Res. 1(2) (1976) 130-143.
    • (1976) Math. Oper. Res. , vol.1 , Issue.2 , pp. 130-143
    • Robinson, S.M.1
  • 34
    • 0040319049 scopus 로고
    • A Monotone convex analogue of linear algebra
    • W. Fenchel (ed.): Copenhagen
    • R. T. Rockafellar: A Monotone convex analogue of linear algebra, In: W. Fenchel (ed.): Proceedings of the Colloquium on Convexity, Copenhagen (1965) 261-276.
    • (1965) Proceedings of the Colloquium on Convexity , pp. 261-276
    • Rockafellar, R.T.1
  • 36
    • 0003350183 scopus 로고
    • Conjugate Duality and Optimization
    • R. T. Rockafellar: Conjugate Duality and Optimization, SIAM, 1974.
    • (1974) SIAM
    • Rockafellar, R.T.1
  • 38
    • 0031529488 scopus 로고    scopus 로고
    • Convex analysis of spectrally defined matrix functions
    • A. Seeger: Convex analysis of spectrally defined matrix functions, SIAM J. Optim. 7(3) (1997) 679-696.
    • (1997) SIAM J. Optim. , vol.7 , Issue.3 , pp. 679-696
    • Seeger, A.1
  • 39
    • 0031139858 scopus 로고    scopus 로고
    • First and second order analysis of nonlinear semidefinite programs
    • A. Shapiro: First and second order analysis of nonlinear semidefinite programs, Math. Programming 77 (1997) 301-320.
    • (1997) Math. Programming , vol.77 , pp. 301-320
    • Shapiro, A.1
  • 40
    • 0031513856 scopus 로고    scopus 로고
    • On uniqueness of Lagrange multipliers in optimization problems subject to cone constraints
    • A. Shapiro: On uniqueness of Lagrange multipliers in optimization problems subject to cone constraints, SIAM J. Optim. 7(2) (1997) 508-518.
    • (1997) SIAM J. Optim. , vol.7 , Issue.2 , pp. 508-518
    • Shapiro, A.1
  • 41
    • 9744282140 scopus 로고
    • Subdifferential calculus of convex operators
    • M. Thera: Subdifferential calculus of convex operators, J. Math. Anal. Appl. 80(1) (1981) 78-91.
    • (1981) J. Math. Anal. Appl. , vol.80 , Issue.1 , pp. 78-91
    • Thera, M.1
  • 42
    • 84974232172 scopus 로고
    • Continuity properties of vector-valued convex functions
    • L. I. Trudzik: Continuity properties of vector-valued convex functions, J. Austral. Math. Soc. (Series A) 36(3) (1984) 404-415.
    • (1984) J. Austral. Math. Soc. (Series A) , vol.36 , Issue.3 , pp. 404-415
    • Trudzik, L.I.1
  • 43
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. Vandenberghe, S. Boyd: Semidefinite programming, SIAM Review 38(1) (1996) 49-95.
    • (1996) SIAM Review , vol.38 , Issue.1 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.