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Volumn 111, Issue 1-2, 2008, Pages 113-140

Invariance and efficiency of convex representations

Author keywords

Central path; Convex optimization; Interior point methods; Semidefinite programming; Semidefinite representations

Indexed keywords

MATHEMATICAL OPERATORS; NUMBER THEORY; PROBLEM SOLVING; SET THEORY; VECTORS;

EID: 34347257132     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0072-6     Document Type: Conference Paper
Times cited : (23)

References (23)
  • 3
    • 33750901124 scopus 로고    scopus 로고
    • A new notion of weighted centers for semidefinite programming
    • in press
    • Chua, C.B.: A new notion of weighted centers for semidefinite programming. SIAM J. Optim. (in press)
    • SIAM J. Optim
    • Chua, C.B.1
  • 4
    • 2442526073 scopus 로고    scopus 로고
    • Relating homogeneous cones and positive definite cones via T-algebras
    • Chua, C.B.: Relating homogeneous cones and positive definite cones via T-algebras. SIAM I Optim. 14, 500-506 (2004)
    • (2004) SIAM I Optim , vol.14 , pp. 500-506
    • Chua, C.B.1
  • 5
    • 34347243450 scopus 로고    scopus 로고
    • Chua, C.B.: An algebraic perspective on homogeneous cone programming, and the primal-dual second order cone approximations algorithm for symmetric cone programming. Ph.D. Thesis, Cornell University, May 2003
    • Chua, C.B.: An algebraic perspective on homogeneous cone programming, and the primal-dual second order cone approximations algorithm for symmetric cone programming. Ph.D. Thesis, Cornell University, May 2003
  • 7
    • 0036848730 scopus 로고    scopus 로고
    • On Nesterov's approach to semi-infinite programming
    • Faybusovich, L.: On Nesterov's approach to semi-infinite programming. Acta Appl. Math. 74, 195-215 (2002)
    • (2002) Acta Appl. Math , vol.74 , pp. 195-215
    • Faybusovich, L.1
  • 8
    • 0031145491 scopus 로고    scopus 로고
    • Hyperbolic polynomials and interior point methods for convex programming
    • Gtller, O.: Hyperbolic polynomials and interior point methods for convex programming. Math. Oper. Res. 22, 350-377 (1997)
    • (1997) Math. Oper. Res , vol.22 , pp. 350-377
    • Gtller, O.1
  • 9
    • 24944516954 scopus 로고    scopus 로고
    • Linear matrix inequality representation of sets
    • Helton, J.W., Vinnikov, V.: Linear matrix inequality representation of sets, 'technical Report (2002)
    • (2002) technical Report
    • Helton, J.W.1    Vinnikov, V.2
  • 11
    • 0033421616 scopus 로고    scopus 로고
    • Polynomial convergence of a new family of primal-dual algorithms for semidefinite programming
    • Monteiro, R.D.C., Tsuchiya, T.: Polynomial convergence of a new family of primal-dual algorithms for semidefinite programming. SIAM J. Optim. 9, 551-577 (1999)
    • (1999) SIAM J. Optim , vol.9 , pp. 551-577
    • Monteiro, R.D.C.1    Tsuchiya, T.2
  • 12
    • 0343714760 scopus 로고    scopus 로고
    • General interior-point maps and existence of weighted paths for nonlinear semidefinite complementarity problems
    • Monteiro, R.D.C., Zanjácomo, P.: General interior-point maps and existence of weighted paths for nonlinear semidefinite complementarity problems. Math. Oper. Res. 25, 381-399 (2000)
    • (2000) Math. Oper. Res , vol.25 , pp. 381-399
    • Monteiro, R.D.C.1    Zanjácomo, P.2
  • 13
    • 1642633464 scopus 로고    scopus 로고
    • Implementation of primal-dual methods for semidefinite programming based on Monteiro and Tsuchiya Newton directions and their variants
    • Monteiro, R.D.C., Zanjácomo, P.: Implementation of primal-dual methods for semidefinite programming based on Monteiro and Tsuchiya Newton directions and their variants. Optim. Method. Soft. 11/12, 91-140 (1999)
    • (1999) Optim. Method. Soft , vol.11-12 , pp. 91-140
    • Monteiro, R.D.C.1    Zanjácomo, P.2
  • 15
    • 0031073753 scopus 로고    scopus 로고
    • Self-scaled barriers and interior-point methods for convex programming
    • Nesterov, Yu.E., Todd, M.J.: Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22, 1-46 (1997)
    • (1997) Math. Oper. Res , vol.22 , pp. 1-46
    • Nesterov, Y.E.1    Todd, M.J.2
  • 16
    • 21344441658 scopus 로고    scopus 로고
    • Pataki, G.: Cone LP's and semidefinite programs: Geometry and a simplex type method. In: Cunningham, W.H., McCormick, S.T., Queyranne, M. Proceedings of the Fifth IPCO Conference, (eds.) pp. 161-174. Springer, Berlin Heidelberg New York (1996)
    • Pataki, G.: Cone LP's and semidefinite programs: Geometry and a simplex type method. In: Cunningham, W.H., McCormick, S.T., Queyranne, M. Proceedings of the Fifth IPCO Conference, (eds.) pp. 161-174. Springer, Berlin Heidelberg New York (1996)
  • 17
    • 31944433002 scopus 로고    scopus 로고
    • Hyperbolic programs, and their derivative relaxations
    • Renegar, J.: Hyperbolic programs, and their derivative relaxations. Found. Comput. Math. 6, 59-79 (2006)
    • (2006) Found. Comput. Math , vol.6 , pp. 59-79
    • Renegar, J.1
  • 18
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 19
    • 21244456109 scopus 로고    scopus 로고
    • Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers
    • Truong, V.A., Tunçel, L.: Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers. Math. Prog. A 100, 295-316 (2004)
    • (2004) Math. Prog. A , vol.100 , pp. 295-316
    • Truong, V.A.1    Tunçel, L.2
  • 20
    • 15844422681 scopus 로고    scopus 로고
    • Strengthened existence and uniqueness conditions for search directions in semidefinite programming
    • Tunçel, L. Wolkowicz H: Strengthened existence and uniqueness conditions for search directions in semidefinite programming. Linear Algebra Appl. 400, 31-60 (2005)
    • (2005) Linear Algebra Appl , vol.400 , pp. 31-60
    • Tunçel, L.1    Wolkowicz, H.2
  • 21
    • 0035351662 scopus 로고    scopus 로고
    • On homogeneous convex cones, the Carathéodory number, and the duality mapping
    • Tunçel, L., Xu, S.: On homogeneous convex cones, the Carathéodory number, and the duality mapping. Math. Oper. Res. 26, 234-247 (2001)
    • (2001) Math. Oper. Res , vol.26 , pp. 234-247
    • Tunçel, L.1    Xu, S.2
  • 22
    • 0001517245 scopus 로고
    • The theory of homogeneous cones
    • Vinberg, È.B.: The theory of homogeneous cones. Trans. Moscow Math. Soc. 12, 340-403 (1965)
    • (1965) Trans. Moscow Math. Soc , vol.12 , pp. 340-403
    • Vinberg, E.B.1
  • 23
    • 0008807868 scopus 로고
    • Self-adjoint determinantal representations of real plane curves
    • Vinnikov, V.: Self-adjoint determinantal representations of real plane curves. Math. Ann. 296, 453-479 (1993)
    • (1993) Math. Ann , vol.296 , pp. 453-479
    • Vinnikov, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.