A class of problems for which cyclic relaxation converges linearly

Computational Optimization and Applications

Volumn 41, Issue 1, 2008, Pages 53-60

  Rautenbach, Dieter ^a   Szegedy, Christian ^b  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

^b CADENCE DESIGN SYSTEMS   (United States)

Author keywords

Coordinate relaxation; Cyclic relaxation; Linear convergence; Method of alternating variables

Indexed keywords

COORDINATE RELAXATION; CYCLIC RELAXATION; LINEAR CONVERGENCE; METHOD OF ALTERNATING VARIABLES; OPTIMUM SOLUTIONS; SEVERAL VARIABLES;

EID: 48349129415     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9094-0     Document Type: Article

References (13)

1. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming-Theory and Algorithms. Wiley, New York (1993)
2. Chen, C.-P., Chu, C.C.N., Wong, D.F.: Fast and exact simultaneous gate and wire sizing by Lagrangian relaxation. In: Proceedings of the 1998 IEEE/ACM International Conference on Computer-Aided Design, pp. 617-624 (1998)
3. Chu, C.C.N., Wong, D.F.: Greedy wire-sizing is linear time. In: Proceedings of the 1998 International Symposium on Physical Design, pp. 39-44 (1998)
4. Cong, J., He, L.: Local-refinement-based optimization with application to device and interconnect sizing. IEEE Trans. Comput.-Aided Design 18, 406-420 (1999)
5. Langkau, K.: Gate-sizing in VLSI-design. Diploma thesis, University of Bonn, Germany (2000), 78 pp. (in German)
6. Luo, Z.Q., Tseng, P.: On the convergence of the coordinate descent method for convex differentiable minimization. J. Optim. Theory Appl. 72, 7-35 (1992)
7. Minoux, M.: Mathematical Programming: Theory and Algorithms. Wiley, Chichester (1986)
8. Polyak, B.T.: A general method of solving extremum problems. Dokl. Akad. Nauk SSSR 174(1), 33-36 (1967) (in Russian). Translated in Sov. Math. Dokl. 8(3) 593-597 (1967)
9. Polyak, B.T.: Minimization of unsmooth functionals. USSR Comput. Math. Math. Phys. 9, 14-29 (1969)
10. Sechen, C., Tennakoon, H.: Gate sizing using Lagrangian relaxation combined with a fast gradient-based pre-processing step. In: Proceedings of the 2002 IEEE/ACM International Conference on Computer-Aided Design, pp. 395-402 (2002)
11. Sutti, C.: Remarks on the convergence of cyclic coordinate methods. Riv. Mat. Univ. Parma IV Ser. 9, 167-172 (1983)
12. Tseng, P.: Convergence of block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109, 475-494 (2001)
13. Yin, X.: Global convergence of the coordinate relaxation method for nongradient mappings. Commun. Appl. Nonlinear Anal. 13, 85-96 (2006)