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Volumn 23, Issue 2, 1998, Pages 339-358

On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues

Author keywords

Eigenvalue optimization; Maximum eigenvalue; Nonsmooth optimization; Semidefinite programming; Sum of eigenvalues

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; MATRIX ALGEBRA; OPTIMIZATION;

EID: 0032070507     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.23.2.339     Document Type: Article
Times cited : (339)

References (26)
  • 1
    • 0003169116 scopus 로고
    • Interior point methods in semidefmite programming with applications to combinatorial optimization
    • Alizadeh, F. (1995). Interior point methods in semidefmite programming with applications to combinatorial optimization. SIAM J. Optim. 5 13-51.
    • (1995) SIAM J. Optim. , vol.5 , pp. 13-51
    • Alizadeh, F.1
  • 2
    • 0031141136 scopus 로고    scopus 로고
    • Complementarity and nondegeneracy in semidefinite programming
    • _, J.-P. Haeberly, M. Overton (1997). Complementarity and nondegeneracy in semidefinite programming. Math. Programming 77 111-128.
    • (1997) Math. Programming , vol.77 , pp. 111-128
    • Haeberly, J.-P.1    Overton, M.2
  • 4
    • 0003008848 scopus 로고
    • Cones of diagonally dominant matrices
    • Barker, G. P., D. Carlson (1975). Cones of diagonally dominant matrices, Pacific J. Math., 57 15-32.
    • (1975) Pacific J. Math. , vol.57 , pp. 15-32
    • Barker, G.P.1    Carlson, D.2
  • 6
    • 0016624432 scopus 로고
    • The minimization of certain nondifferentiable sums of eigenvalue problems
    • Cullum, J., W. E. Donath, P. Wolfe (1975). The minimization of certain nondifferentiable sums of eigenvalue problems. Math. Programming Stud. 3 35-55.
    • (1975) Math. Programming Stud. , vol.3 , pp. 35-55
    • Cullum, J.1    Donath, W.E.2    Wolfe, P.3
  • 7
    • 34250080270 scopus 로고
    • Laplacian eigenvalues and the maximum cut problem
    • Delorme, C., S. Poljak (1993). Laplacian eigenvalues and the maximum cut problem. Math. Programming 62 557-574.
    • (1993) Math. Programming , vol.62 , pp. 557-574
    • Delorme, C.1    Poljak, S.2
  • 8
    • 21844488492 scopus 로고
    • Sensitivity analysis of all eigenvalues of a symmetric matrix
    • Hiriart-Urruty, J.-B., D. Ye (1995). Sensitivity analysis of all eigenvalues of a symmetric matrix. Numer. Math. 70 45-72.
    • (1995) Numer. Math. , vol.70 , pp. 45-72
    • Hiriart-Urruty, J.-B.1    Ye, D.2
  • 11
    • 0000142610 scopus 로고
    • On a theorem of Weyl concerning the eigenvalues of linear transformations
    • Ky Fan (1949). On a theorem of Weyl concerning the eigenvalues of linear transformations. Proc. Nat. Acad. Sci. USA 35 652-655.
    • (1949) Proc. Nat. Acad. Sci. USA , vol.35 , pp. 652-655
    • Fan, K.1
  • 12
    • 0030304775 scopus 로고    scopus 로고
    • Convex analysis on the Hermitian matrices
    • Lewis, A. S. (1996). Convex analysis on the Hermitian matrices. SIAM J. Optim. 6 164-177.
    • (1996) SIAM J. Optim. , vol.6 , pp. 164-177
    • Lewis, A.S.1
  • 13
    • 0042602157 scopus 로고    scopus 로고
    • Eigenvalue optimization
    • _, M. Overton (1996). Eigenvalue optimization. Acta Numerica 5 149-190.
    • (1996) Acta Numerica , vol.5 , pp. 149-190
    • Overton, M.1
  • 15
    • 0003181133 scopus 로고
    • Large-scale optimization of eigenvalues
    • Overton, M. L. (1992). Large-scale optimization of eigenvalues. SIAM J. Optim. 2 88-120.
    • (1992) SIAM J. Optim. , vol.2 , pp. 88-120
    • Overton, M.L.1
  • 16
    • 1942497666 scopus 로고
    • On the sum of the largest eigenvalues of a symmetric matrix
    • _, R. S. Womersley (1992). On the sum of the largest eigenvalues of a symmetric matrix. SIAM J. Matrix Anal. Appl. 1341-45.
    • (1992) SIAM J. Matrix Anal. Appl. , pp. 1341-1345
    • Womersley, R.S.1
  • 17
    • 34250080273 scopus 로고
    • Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices
    • _, _ (1993). Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices. Math. Programming 62 321-357.
    • (1993) Math. Programming , vol.62 , pp. 321-357
  • 18
    • 0040730891 scopus 로고
    • Management Science Research Report MSRR-#595, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA
    • Pataki, G. (1994). On the facial structure of cone-LPs and semidefinite programs. Management Science Research Report MSRR-#595, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA.
    • (1994) On the Facial Structure of Cone-LPs and Semidefinite Programs
    • Pataki, G.1
  • 19
    • 0042839371 scopus 로고
    • Some geometric results in semidefinite programming
    • Ramana, M. V., A. Goldman (1995). Some geometric results in semidefinite programming. J. Global Opt. 7 33-50.
    • (1995) J. Global Opt. , vol.7 , pp. 33-50
    • Ramana, M.V.1    Goldman, A.2
  • 20
    • 0031141179 scopus 로고    scopus 로고
    • A semidefinite framework for trust region subproblems with applications to large scale minimization
    • Rendl, F., H. Wolkowicz (1997). A semidefinite framework for trust region subproblems with applications to large scale minimization. Math. Programming 77 273-299.
    • (1997) Math. Programming , vol.77 , pp. 273-299
    • Rendl, F.1    Wolkowicz, H.2
  • 21
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • Rockafellar, R. T. (1970) Convex Analysis, Princeton University Press, Princeton, New Jersey.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 22
    • 0011328005 scopus 로고
    • Extremal problems on the set of nonnegative definite matrices
    • Shapiro, A. (1985). Extremal problems on the set of nonnegative definite matrices. Linear Algebra Appl. 67 7-18.
    • (1985) Linear Algebra Appl. , vol.67 , pp. 7-18
    • Shapiro, A.1
  • 23
    • 0000496360 scopus 로고
    • On eigenvalue optimization
    • _. M. K. H. Fan (1995). On eigenvalue optimization. SIAM J. Optim. 5 552-569.
    • (1995) SIAM J. Optim. , vol.5 , pp. 552-569
    • Fan, M.K.H.1
  • 25
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • Vandenberghe, L., S. Boyd (1996). Semidefinite programming. SIAM Rev. 38 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 26
    • 0000890903 scopus 로고
    • Some applications of optimization in matrix theory
    • Wolkowicz, H. (1981). Some applications of optimization in matrix theory. Linear Algebra Appl. 40 101-118.
    • (1981) Linear Algebra Appl. , vol.40 , pp. 101-118
    • Wolkowicz, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.