메뉴 건너뛰기




Volumn 15, Issue 3-4, 2001, Pages 175-200

A projected gradient algorithm for solving the maxcut SDP relaxation

Author keywords

Approximation algorithm; Maxcut; Projected gradient method; Semidefinite programming; Semidefinite relaxation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; OPTIMIZATION;

EID: 0036457237     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (60)

References (26)
  • 1
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications to combinatorial optimization
    • Alizadeb, F. (1995). Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM Journal on Optimization, 5(1), 13-51.
    • (1995) SIAM Journal on Optimization , vol.5 , Issue.1 , pp. 13-51
    • Alizadeb, F.1
  • 2
    • 0024012514 scopus 로고
    • An application of combinatorial optimization to statistical optimization and circuit layout design
    • Barahona, F., Grötschel, M., Jünger, M. and Reinelt, G. (1988). An application of combinatorial optimization to statistical optimization and circuit layout design. Operations Research, 36(3), 493-513.
    • (1988) Operations Research , vol.36 , Issue.3 , pp. 493-513
    • Barahona, F.1    Grötschel, M.2    Jünger, M.3    Reinelt, G.4
  • 3
    • 0039772219 scopus 로고    scopus 로고
    • Solving large-scale sparse semidefinite programs for combinatorial optimization
    • Research Report, Department of Management Science, University of Iowa, Iowa, To appear
    • Benson, S., Ye, Y. and Zhang, X. Solving large-scale sparse semidefinite programs for combinatorial optimization. Research Report, Department of Management Science, University of Iowa, Iowa, 1998. To appear in SIAM Journal on Optimization.
    • (1998) SIAM Journal on Optimization
    • Benson, S.1    Ye, Y.2    Zhang, X.3
  • 4
    • 0023089597 scopus 로고
    • Efficient algorithms for layer assignment problems
    • Chang, K. C. and Du, D. H. (1987). Efficient algorithms for layer assignment problems. IEEE Transactions on Computer-Aided Design, CAD-6(1), 67-78.
    • (1987) IEEE Transactions on Computer-Aided Design , vol.CAD-6 , Issue.1 , pp. 67-78
    • Chang, K.C.1    Du, D.H.2
  • 5
    • 0020751273 scopus 로고
    • A graph-theoretic via minimization algorithm for two-layer printed circuit boards
    • Chen, R., Kajitani, Y. and Chan, S. (1983). A graph-theoretic via minimization algorithm for two-layer printed circuit boards. IEEE Transactions on Circuits and Systems, CAS-30(5), 284-299.
    • (1983) IEEE Transactions on Circuits and Systems , vol.CAS-30 , Issue.5 , pp. 284-299
    • Chen, R.1    Kajitani, Y.2    Chan, S.3
  • 6
    • 0000201892 scopus 로고    scopus 로고
    • Semidefinite programming relaxation for nonconvex quadratic programs
    • Fujie, T. and Kojima, M. (1997). Semidefinite programming relaxation for nonconvex quadratic programs. J. Global Optim., 10, 168-189.
    • (1997) J. Global Optim. , vol.10 , pp. 168-189
    • Fujie, T.1    Kojima, M.2
  • 7
    • 0000419029 scopus 로고    scopus 로고
    • Numerical evaluation of SDPA (Semidefinite Programming Algorithm)
    • Frenk, H., Roos, K., Terlaky, T. and Zhang, S. Editors, Kluwer Academic Press
    • Fujisawa, K., Fukuda, M., Kojima, M. and Nakata, K. (1999). Numerical evaluation of SDPA (Semidefinite Programming Algorithm). In: Frenk, H., Roos, K., Terlaky, T. and Zhang, S. Editors, High Performance Optimization, pp. 267-301. Kluwer Academic Press.
    • (1999) High Performance Optimization , pp. 267-301
    • Fujisawa, K.1    Fukuda, M.2    Kojima, M.3    Nakata, K.4
  • 8
    • 0000609227 scopus 로고    scopus 로고
    • Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
    • Fujisawa, K., Kojima, M. and Nakata, K. (1997). Exploiting sparsity in primal-dual interior-point methods for semidefinite programming. Mathematical Programming, 79, 235-253.
    • (1997) Mathematical Programming , vol.79 , pp. 235-253
    • Fujisawa, K.1    Kojima, M.2    Nakata, K.3
  • 9
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • Goemans, M. X. and Williamson, D. P. (1995). Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of ACM, 1115-1145, 42.
    • (1995) Journal of ACM , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 11
    • 0034415006 scopus 로고    scopus 로고
    • A spectral bundle method for semidefinite programming
    • Helmberg, C. and Rendl, F. (2000). A spectral bundle method for semidefinite programming. SIAM Journal on Optimization, 10, 673-696.
    • (2000) SIAM Journal on Optimization , vol.10 , pp. 673-696
    • Helmberg, C.1    Rendl, F.2
  • 13
    • 0012031279 scopus 로고    scopus 로고
    • Solving graph bisection problems with semidefinite programming
    • Department of Computer Sciences, University of Copenhagen, July
    • Karisch, S. E., Rendl, F. and Clausen, J., Solving graph bisection problems with semidefinite programming. Technical Report DIKU-TR-97/9, Department of Computer Sciences, University of Copenhagen, July 1997.
    • (1997) Technical Report DIKU-TR-97/9
    • Karisch, S.E.1    Rendl, F.2    Clausen, J.3
  • 15
    • 0042185149 scopus 로고    scopus 로고
    • An incomplete cholesky factorization for dense matrices
    • Chih-Jen Lin and Romesh Saigal (2000). An incomplete cholesky factorization for dense matrices. BIT, 40, 536-558.
    • (2000) BIT , vol.40 , pp. 536-558
    • Lin, C.-J.1    Saigal, R.2
  • 16
    • 0018292109 scopus 로고
    • On the Shannon Capacity of a graph
    • January
    • Lovász, L., On the Shannon Capacity of a graph. IEEE Transactions of Information Theory, IT-25(1), 1-7, January 1979.
    • (1979) IEEE Transactions of Information Theory , vol.IT-25 , Issue.1 , pp. 1-7
    • Lovász, L.1
  • 17
    • 0001154274 scopus 로고
    • Cones of matrices and setfunctions, and 0-1 optimization
    • Lovász, L. and Schrijver, A. (1991). Cones of matrices and setfunctions, and 0-1 optimization. SIAM Journal on Optimization, 1, 166-190.
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 18
    • 0031681870 scopus 로고    scopus 로고
    • Semidenite relaxation and nonconvex quadratic optimization
    • Nesterov, Y. (1998). Semidenite relaxation and nonconvex quadratic optimization. Optimization Methods and Software, 9, 141-160.
    • (1998) Optimization Methods and Software , vol.9 , pp. 141-160
    • Nesterov, Y.1
  • 19
    • 0001870308 scopus 로고    scopus 로고
    • Design and performance of parallel and distributed approximation algorithms for maxcut
    • Peinado, M. and Homer, S. (1997). Design and performance of parallel and distributed approximation algorithms for maxcut. Journal of Parallel and Distributed Computing, 46, 48-61.
    • (1997) Journal of Parallel and Distributed Computing , vol.46 , pp. 48-61
    • Peinado, M.1    Homer, S.2
  • 20
    • 0021482729 scopus 로고
    • Optimal layer assignment for interconnect
    • Pinter, R. Y. (1984). Optimal layer assignment for interconnect. J. VLSI Comput. Syst., 1, 123-137.
    • (1984) J. VLSI Comput. Syst. , vol.1 , pp. 123-137
    • Pinter, R.Y.1
  • 21
    • 0002821681 scopus 로고
    • A recipe for semidefinite relaxation for 0-1 quadratic programming
    • Poljak, S., Rendl, F. and Wolkowicz, H. (1995). A recipe for semidefinite relaxation for 0-1 quadratic programming. Journal of Global Optimization, 7, 51-73.
    • (1995) Journal of Global Optimization , vol.7 , pp. 51-73
    • Poljak, S.1    Rendl, F.2    Wolkowicz, H.3
  • 22
    • 0011588477 scopus 로고
    • Maximum cuts and large bipartite subgraphs
    • New Brunswick, NJ
    • Poljak, S. and Tuza, Z., Maximum cuts and large bipartite subgraphs. In: Combinatorial Optimization (New Brunswick, NJ, 1992-1993), pp. 181-244.
    • (1992) Combinatorial Optimization , pp. 181-244
    • Poljak, S.1    Tuza, Z.2
  • 23
    • 0003744099 scopus 로고
    • Providence, RI
    • Amer. Math. Soc., Providence, RI, 1995.
    • (1995) Amer. Math. Soc.
  • 25
    • 0000471367 scopus 로고
    • Originally published
    • Originally published in Tekhnicheskaya Kibernetika, No. 1, 1987, pp. 128-139.
    • (1987) Tekhnicheskaya Kibernetika , Issue.1 , pp. 128-139
  • 26
    • 0000549997 scopus 로고    scopus 로고
    • Approximating quadratic programming with quadratic constraints
    • Ye, Y. (1999). Approximating quadratic programming with quadratic constraints. Mathematical Programming, 84, 219-226.
    • (1999) Mathematical Programming , vol.84 , pp. 219-226
    • Ye, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.