메뉴 건너뛰기




Volumn 106, Issue 3, 2006, Pages 527-545

On the behavior of the homogeneous self-dual model for conic convex optimization

Author keywords

Conic Optimization; Convex Cone; Convex Optimization; Duality; Level Sets; Self Dual Embedding; self scaled Cone

Indexed keywords

LOGIC PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING; SET THEORY;

EID: 33644544399     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-005-0667-3     Document Type: Article
Times cited : (12)

References (19)
  • 1
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications to combinatorial optimization
    • Alizadeh, F.: Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optimization 5 (1), 13-51 (1995)
    • (1995) SIAM J. Optimization , vol.5 , Issue.1 , pp. 13-51
    • Alizadeh, F.1
  • 2
    • 33644541992 scopus 로고    scopus 로고
    • On two measures of problem complexity and their explanatory value for the performance of SeDuMi on second-order cone problems
    • To appear in Computational Optimization and Applications
    • Cai, Z., Freund, R.M.: On two measures of problem complexity and their explanatory value for the performance of SeDuMi on second-order cone problems. MIT Operations Research Center Working Paper OR-371-04. To appear in Computational Optimization and Applications
    • MIT Operations Research Center Working Paper , vol.OR-371-04
    • Cai, Z.1    Freund, R.M.2
  • 3
    • 0242679721 scopus 로고    scopus 로고
    • On the primal-dual geometry of level sets in linear and conic optimization
    • Freund, R.M.: On the primal-dual geometry of level sets in linear and conic optimization. SIAM J. Optimization 13 (4), 1004-1013 (2003)
    • (2003) SIAM J. Optimization , vol.13 , Issue.4 , pp. 1004-1013
    • Freund, R.M.1
  • 4
    • 0000553640 scopus 로고    scopus 로고
    • Some characterizations and properties of the "distance to ill-posedness" and the condition measure of a conic linear system
    • Freund, R.M., Vera, J.R.: Some characterizations and properties of the "distance to ill-posedness" and the condition measure of a conic linear system. Math. Program. 86, 225-260 (1999)
    • (1999) Math. Program. , vol.86 , pp. 225-260
    • Freund, R.M.1    Vera, J.R.2
  • 5
    • 0000921195 scopus 로고    scopus 로고
    • Initialization in semidefinite programming via a self-dual, skew-symmetric embedding
    • de Klerk, E., Roos, C., Terlaky, T.: Initialization in semidefinite programming via a self-dual, skew-symmetric embedding. Oper. Res. Lett. 20 (5), 213-221 (1997)
    • (1997) Oper. Res. Lett. , vol.20 , Issue.5 , pp. 213-221
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 6
    • 0001624064 scopus 로고    scopus 로고
    • Infeasible-start semidefinite programming algorithms via self-dual embeddings
    • Fields Institute Communications (18), American Mathematical Society, H. Wolkowicz, P.M. Pardalos (eds.)
    • de Klerk, E., Roos, C., Terlaky, T.: Infeasible-start semidefinite programming algorithms via self-dual embeddings. Fields Institute Communications (18), American Mathematical Society, H. Wolkowicz, P.M. Pardalos (eds.), Topics in Semidefinite and Interior Point Methods, 1998, pp. 215-237
    • (1998) Topics in Semidefinite and Interior Point Methods , pp. 215-237
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 7
    • 0344528808 scopus 로고    scopus 로고
    • Self-dual embeddings
    • H. Wolkowicz, R. Saigal, L. Vandenberghe, (eds.), Kluwer Academic Publishers
    • de Klerk, E., Roos, C., Terlaky, T.: Self-dual embeddings. In: Handbook of Semidefinite Programming H. Wolkowicz, R. Saigal, L. Vandenberghe, (eds.), Kluwer Academic Publishers, 2000, pp. 111-138
    • (2000) Handbook of Semidefinite Programming , pp. 111-138
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 8
    • 0003493478 scopus 로고    scopus 로고
    • Duality and self-duality for conic convex programming
    • Erasmus University Rotterdam, The Netherlands, March
    • Luo, Z.-Q., Sturm, J.F., Zhang, S.: Duality and self-duality for conic convex programming. Technical Report, Erasmus University Rotterdam, The Netherlands, March 1996
    • (1996) Technical Report
    • Luo, Z.-Q.1    Sturm, J.F.2    Zhang, S.3
  • 9
    • 0039314596 scopus 로고    scopus 로고
    • Long-step strategies in interior-point primal-dual methods
    • Nesterov, Y.: Long-step strategies in interior-point primal-dual methods. Math. Program. 76, 47-94 (1996)
    • (1996) Math. Program. , vol.76 , pp. 47-94
    • Nesterov, Y.1
  • 11
    • 0031073753 scopus 로고    scopus 로고
    • Self-scaled barriers and interior-point methods for convex programming
    • Nesterov, Y., Todd, M.J., Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22, 1-42 (1997)
    • (1997) Math. Oper. Res. , vol.22 , pp. 1-42
    • Nesterov, Y.1    Todd, M.J.2
  • 12
    • 0032222088 scopus 로고    scopus 로고
    • Primal-dual interior-point methods for self-scaled cones
    • Nesterov, Y., Todd, M.J.: Primal-dual interior-point methods for self-scaled cones. SIAM J. Optimization 8, 324-364 (1998)
    • (1998) SIAM J. Optimization , vol.8 , pp. 324-364
    • Nesterov, Y.1    Todd, M.J.2
  • 13
    • 0031698662 scopus 로고    scopus 로고
    • On homogeneous interior-point algorithms for semidefinite programming
    • Potra, F.A., Sheng, R.: On homogeneous interior-point algorithms for semidefinite programming. Optimization Meth. Software 9, 161-184 (1998)
    • (1998) Optimization Meth. Software , vol.9 , pp. 161-184
    • Potra, F.A.1    Sheng, R.2
  • 14
    • 0028426653 scopus 로고
    • Some perturbation theory for linear programming
    • Renegar, J.: Some perturbation theory for linear programming. Math. Program. 65 (1), 73-91 (1994)
    • (1994) Math. Program. , vol.65 , Issue.1 , pp. 73-91
    • Renegar, J.1
  • 15
    • 0036923521 scopus 로고    scopus 로고
    • Implementation of interior point methods for mixed semidefinite and second order cone optimization problems
    • Sturm, J.F.: Implementation of interior point methods for mixed semidefinite and second order cone optimization problems. Optimization Meth. Software 17 (6), 1105-1154 (2002)
    • (2002) Optimization Meth. Software , vol.17 , Issue.6 , pp. 1105-1154
    • Sturm, J.F.1
  • 16
    • 0012595684 scopus 로고
    • A centered projective algorithm for linear programming
    • Todd, M.J., Ye, Y.: A centered projective algorithm for linear programming. Math. Oper. Res. 15, 508-529 (1990)
    • (1990) Math. Oper. Res. , vol.15 , pp. 508-529
    • Todd, M.J.1    Ye, Y.2
  • 17
    • 21344457406 scopus 로고    scopus 로고
    • A simplified homogeneous and self-dual linear programming algorithm and its implementation
    • Xu, X., Hung, P.-F., Ye, Y.: A simplified homogeneous and self-dual linear programming algorithm and its implementation. Ann. Oper. Res. 62, 151-171 (1996)
    • (1996) Ann. Oper. Res. , vol.62 , pp. 151-171
    • Xu, X.1    Hung, P.-F.2    Ye, Y.3
  • 18
    • 0003058678 scopus 로고
    • An O(√nL)-iteration homogeneous and self-dual linear programming algorithm
    • Ye, Y., Todd, M.J., Mizuno, S.: An O(√nL)-iteration homogeneous and self-dual linear programming algorithm. Math. Oper. Res. 19, 53-67 (1994)
    • (1994) Math. Oper. Res. , vol.19 , pp. 53-67
    • Ye, Y.1    Todd, M.J.2    Mizuno, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.