메뉴 건너뛰기




Volumn 36, Issue 2-3, 2007, Pages 289-307

A conversion of an SDP having free variables into the standard form SDP

Author keywords

Conversion; Equality constraint; Primal dual interior point method; Semidefinite program; Standard form

Indexed keywords

CONSTRAINT THEORY; NUMERICAL METHODS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

EID: 34248364413     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-006-9002-z     Document Type: Article
Times cited : (7)

References (22)
  • 3
    • 0033295839 scopus 로고    scopus 로고
    • SDPLIB 1.2, a library of semidefinite programming test problems
    • Borchers, B.: SDPLIB 1.2, a library of semidefinite programming test problems. Optim. Methods Software 11&12, 683-690 (1999)
    • (1999) Optim. Methods Software , vol.11-12 , pp. 683-690
    • Borchers, B.1
  • 4
    • 0000419029 scopus 로고    scopus 로고
    • Numerical evaluation of SDPA (SemiDefinite Programming Algorithm)
    • Frenk, H, Roos, K, Terlaky, T, Zhang, S, eds, Kluwer Academic, Dordrecht
    • Fujisawa, K., Fukuda, M., Kojima, M., Nakata, K.: Numerical evaluation of SDPA (SemiDefinite Programming Algorithm). In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds.) High Performance Optimization, pp. 267-301. Kluwer Academic, Dordrecht (2000)
    • (2000) High Performance Optimization , pp. 267-301
    • Fujisawa, K.1    Fukuda, M.2    Kojima, M.3    Nakata, K.4
  • 5
    • 0000609227 scopus 로고    scopus 로고
    • Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
    • Fujisawa, K., Kojima, M., Nakata, K.: Exploiting sparsity in primal-dual interior-point methods for semidefinite programming, Math. Program. 79, 235-253 (1997)
    • (1997) Math. Program , vol.79 , pp. 235-253
    • Fujisawa, K.1    Kojima, M.2    Nakata, K.3
  • 7
    • 0035238840 scopus 로고    scopus 로고
    • Exploiting sparsity in semidefinite programming via matrix completion I: General framework
    • Fukuda, M., Kojima, M., Murota, K., Nakata, K.: Exploiting sparsity in semidefinite programming via matrix completion I: General framework. SIAM J. Optim. 11, 647-674 (2000)
    • (2000) SIAM J. Optim , vol.11 , pp. 647-674
    • Fukuda, M.1    Kojima, M.2    Murota, K.3    Nakata, K.4
  • 8
    • 34248357662 scopus 로고    scopus 로고
    • Helmberg, C.: Semidefinite programming for combinatorial optimization. Habilitationsschrift. ZIP Report ZR-0034, TU Berlin, Konrad-Zuse-Zentrum, Berlin (2000). Available at http://www.zip.de/PaperWeb/abstracts/ZR-0034/
    • Helmberg, C.: Semidefinite programming for combinatorial optimization. Habilitationsschrift. ZIP Report ZR-0034, TU Berlin, Konrad-Zuse-Zentrum, Berlin (2000). Available at http://www.zip.de/PaperWeb/abstracts/ZR-0034/
  • 10
    • 0031542833 scopus 로고    scopus 로고
    • Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices
    • Kojima, M., Shindoh, S., Hara, S.: Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. SIAM J. Optim. 7, 86-125 (1997)
    • (1997) SIAM J. Optim , vol.7 , pp. 86-125
    • Kojima, M.1    Shindoh, S.2    Hara, S.3
  • 11
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problems of moments
    • Lasserre, J.B.: Global optimization with polynomials and the problems of moments. SIAM J. Optim. 11, 796-817 (2001)
    • (2001) SIAM J. Optim , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 12
    • 0031285899 scopus 로고    scopus 로고
    • Primal-dual path-following algorithms for semidefinite programming
    • Monteiro, R.D.C.: Primal-dual path-following algorithms for semidefinite programming. SIAM J. Optim. 7, 663-678 (1997)
    • (1997) SIAM J. Optim , vol.7 , pp. 663-678
    • Monteiro, R.D.C.1
  • 13
    • 1542337154 scopus 로고    scopus 로고
    • Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results
    • Nakata, K., Fujisawa, K., Fukuda, M., Kojima, M., Murota, K.: Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results. Math. Program. 95, 303-327 (2003)
    • (2003) Math. Program , vol.95 , pp. 303-327
    • Nakata, K.1    Fujisawa, K.2    Fukuda, M.3    Kojima, M.4    Murota, K.5
  • 14
    • 29244441161 scopus 로고    scopus 로고
    • A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion
    • Nakata, K., Yamashita, M., Fujisawa, K., Kojima, M.: A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion. Parallel Comput. 32, 24-43 (2006)
    • (2006) Parallel Comput , vol.32 , pp. 24-43
    • Nakata, K.1    Yamashita, M.2    Fujisawa, K.3    Kojima, M.4
  • 15
    • 0035872736 scopus 로고    scopus 로고
    • Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm
    • Nakata, M., Nakatsuji, H., Ehara, M., Fukuda, M., Nakata, K., Fujisawa, K.: Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm. J. Chem. Phys. 114, 8282-8292 (2001)
    • (2001) J. Chem. Phys , vol.114 , pp. 8282-8292
    • Nakata, M.1    Nakatsuji, H.2    Ehara, M.3    Fukuda, M.4    Nakata, K.5    Fujisawa, K.6
  • 16
    • 0032222088 scopus 로고    scopus 로고
    • Primal-dual interior-point methods for self-scaled cones
    • Nesterov, Yu.E., Todd, M.J.: Primal-dual interior-point methods for self-scaled cones. SIAM J. Optim. 8, 324-364 (1998)
    • (1998) SIAM J. Optim , vol.8 , pp. 324-364
    • Nesterov, Y.E.1    Todd, M.J.2
  • 17
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Software 11&12, 625-653 (1999)
    • (1999) Optim. Methods Software , vol.11-12 , pp. 625-653
    • Sturm, J.F.1
  • 18
    • 3142743708 scopus 로고    scopus 로고
    • Solving semidefinite-quadratic-linear programs using SDPT3
    • Tütüncü, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. 95, 189-217 (2003)
    • (2003) Math. Program , vol.95 , pp. 189-217
    • Tütüncü, R.H.1    Toh, K.C.2    Todd, M.J.3
  • 19
    • 33847158335 scopus 로고    scopus 로고
    • Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity
    • Waki, H., Kim, S., Kojima, M., Muramatsu, M.: Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity. SIAM J. Optim. 17, 218-242 (2006)
    • (2006) SIAM J. Optim , vol.17 , pp. 218-242
    • Waki, H.1    Kim, S.2    Kojima, M.3    Muramatsu, M.4
  • 20
    • 84878541685 scopus 로고    scopus 로고
    • GLOBAL Library: http://www.gamsworld.org/global/globallib.htm
    • GLOBAL Library
  • 21
    • 0027911607 scopus 로고
    • Symmetric indefinite systems for interior point methods
    • Vanderbei, R.J., Carpenter, T.J.: Symmetric indefinite systems for interior point methods. Math. Program. 58, 1-32 (1993)
    • (1993) Math. Program , vol.58 , pp. 1-32
    • Vanderbei, R.J.1    Carpenter, T.J.2
  • 22
    • 0042486152 scopus 로고    scopus 로고
    • Implementation and evaluation of SDPA6.0 (SemiDefinite Programming Algorithm 6.0)
    • Yamashita, M., Fujisawa, K., Kojima, M.: Implementation and evaluation of SDPA6.0 (SemiDefinite Programming Algorithm 6.0). Optim. Methods Software 18, 491-505 (2003)
    • (2003) Optim. Methods Software , vol.18 , pp. 491-505
    • Yamashita, M.1    Fujisawa, K.2    Kojima, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.