메뉴 건너뛰기




Volumn 312, Issue , 2005, Pages 195-238

Interior-point algorithms for semidefinite programming problems derived from the KYP lemma

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR PROGRAMMING; NONLINEAR PROGRAMMING; SIGNAL PROCESSING;

EID: 33750916164     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/10997703_12     Document Type: Article
Times cited : (68)

References (54)
  • 1
    • 0031673619 scopus 로고    scopus 로고
    • Advanced gain-scheduled techniques for uncertain systems
    • P. Apkarian and R. J. Adams (1998). Advanced gain-scheduled techniques for uncertain systems. IEEE Trans. Control Sys. Tech., 6(1):21-32.
    • (1998) IEEE Trans. Control Sys. Tech , vol.6 , Issue.1 , pp. 21-32
    • Apkarian, P.1    Adams, R.J.2
  • 6
    • 0012688640 scopus 로고    scopus 로고
    • Convex optimization problems involving finite autocorrelation sequences
    • B. Alkire and L. Vandenberghe (2002). Convex optimization problems involving finite autocorrelation sequences. Mathematical Programming Series A, 93:331-359.
    • (2002) Mathematical Programming Series A , vol.93 , pp. 331-359
    • Alkire, B.1    Vandenberghe, L.2
  • 9
    • 33947505240 scopus 로고    scopus 로고
    • B. Borchers (2002). CSDP 4.2 User's Guide. Available from www.nmt.edu/~borchers/csdp.html. 10. V. Balakrishnan and L. Vandenberghe (1998). Linear Matrix Inequalities for signal processing: An overview. Proceedings of the 32nd Annual Conference on Information Sciences and Systems, Princeton, New Jersey.
    • B. Borchers (2002). CSDP 4.2 User's Guide. Available from www.nmt.edu/~borchers/csdp.html. 10. V. Balakrishnan and L. Vandenberghe (1998). Linear Matrix Inequalities for signal processing: An overview. Proceedings of the 32nd Annual Conference on Information Sciences and Systems, Princeton, New Jersey.
  • 10
    • 0037248880 scopus 로고    scopus 로고
    • Semidefinite programming duality and linear time-invariant systems
    • V. Balakrishnan and L. Vandenberghe (2003). Semidefinite programming duality and linear time-invariant systems. IEEE Trans. Aut. Control, 48:30-41.
    • (2003) IEEE Trans. Aut. Control , vol.48 , pp. 30-41
    • Balakrishnan, V.1    Vandenberghe, L.2
  • 11
    • 0033349519 scopus 로고    scopus 로고
    • Efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems
    • V. Balakrishnan and F. Wang (1999). Efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems. IEEE Trans. Aut. Control, AC-44(11):2185-2190.
    • (1999) IEEE Trans. Aut. Control , vol.AC-44 , Issue.11 , pp. 2185-2190
    • Balakrishnan, V.1    Wang, F.2
  • 13
    • 0036842590 scopus 로고    scopus 로고
    • Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design
    • T. N. Davidson, Z.-Q. Luo, and J. F. Sturm (2002). Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design. IEEE Transactions on Signal Processing, 50(11):2702-2715.
    • (2002) IEEE Transactions on Signal Processing , vol.50 , Issue.11 , pp. 2702-2715
    • Davidson, T.N.1    Luo, Z.-Q.2    Sturm, J.F.3
  • 14
    • 0020203138 scopus 로고
    • Analysis of feedback systems with structured uncertainties
    • J. Doyle (1982). Analysis of feedback systems with structured uncertainties. IEE Proc., 129-D(6):242-250.
    • (1982) IEE Proc , vol.129-D , Issue.6 , pp. 242-250
    • Doyle, J.1
  • 15
    • 0035503003 scopus 로고    scopus 로고
    • On the parametrization of positive real sequences and MA parameter estimation
    • B. Dumitrescu, I. Tabus, and P. Stoica (2001). On the parametrization of positive real sequences and MA parameter estimation. IEEE Transactions on Signal Processing, 49(11):2630-9.
    • (2001) IEEE Transactions on Signal Processing , vol.49 , Issue.11 , pp. 2630-2639
    • Dumitrescu, B.1    Tabus, I.2    Stoica, P.3
  • 16
    • 0031259375 scopus 로고    scopus 로고
    • Improved Upper Bounds for the Mixed Structured Singular Value
    • M. Fu and N. E. Barabanov (1997). Improved Upper Bounds for the Mixed Structured Singular Value. IEEE Trans. Aut. Control, 42(10):1447-1452.
    • (1997) IEEE Trans. Aut. Control , vol.42 , Issue.10 , pp. 1447-1452
    • Fu, M.1    Barabanov, N.E.2
  • 17
    • 33947542027 scopus 로고    scopus 로고
    • K. Fujisawa, M. Kojima, and K. Nakata (1998). SDPA User's Manual. Available from www.is.titech.ac.jp/~yamashi9/sdpa.
    • K. Fujisawa, M. Kojima, and K. Nakata (1998). SDPA User's Manual. Available from www.is.titech.ac.jp/~yamashi9/sdpa.
  • 18
    • 0025747144 scopus 로고
    • Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics
    • M. K. H. Fan, A. L. Tits, and J. C. Doyle (1991). Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Trans. Aut. Control, AC-36(1):25-38.
    • (1991) IEEE Trans. Aut. Control , vol.AC-36 , Issue.1 , pp. 25-38
    • Fan, M.K.H.1    Tits, A.L.2    Doyle, J.C.3
  • 19
    • 1542319249 scopus 로고    scopus 로고
    • Polynomial complexity for a Nesterov-Todd potential-reduction method with inexact search directions
    • J. Gillberg and A. Hansson (2003). Polynomial complexity for a Nesterov-Todd potential-reduction method with inexact search directions. Proc. IEEE Conference on Decision and Control.
    • (2003) Proc. IEEE Conference on Decision and Control
    • Gillberg, J.1    Hansson, A.2
  • 22
    • 0004141725 scopus 로고
    • Information and System sciences. Prentice Hall, Englewood Cliffs, NJ
    • M. Green and D. J. N. Limebeer (1995). Linear Robust Control. Information and System sciences. Prentice Hall, Englewood Cliffs, NJ.
    • (1995) Linear Robust Control
    • Green, M.1    Limebeer, D.J.N.2
  • 23
    • 33947542297 scopus 로고    scopus 로고
    • P. Cabinet and A. Nemirovskii (1995). LMI Control Toolbox for Matlab. The MathWorks, Inc.
    • P. Cabinet and A. Nemirovskii (1995). LMI Control Toolbox for Matlab. The MathWorks, Inc.
  • 25
    • 85086796258 scopus 로고    scopus 로고
    • ∞-optimal control via finitedimensional Q-parametrization and linear matrix inequalities
    • ∞-optimal control via finitedimensional Q-parametrization and linear matrix inequalities. Proc. American Control Conf.
    • (1999) Proc. American Control Conf
    • Hindi, H.1    Boyd, S.2
  • 27
    • 0034444795 scopus 로고    scopus 로고
    • Efficient solution of linear matrix inequalities for integral quadratic constraints
    • A. Hansson and L. Vandenberghe (2000). Efficient solution of linear matrix inequalities for integral quadratic constraints. Proc. IEEE Conf. on Decision and Control, 5033-5034.
    • (2000) Proc. IEEE Conf. on Decision and Control , pp. 5033-5034
    • Hansson, A.1    Vandenberghe, L.2
  • 28
    • 0034854497 scopus 로고    scopus 로고
    • A primal-dual potential reduction method for integral quadratic constraints
    • Arlington, Virginia
    • A. Hansson and L. Vandenberghe (2001). A primal-dual potential reduction method for integral quadratic constraints. Proc. American Control Conference, 3013-3018, Arlington, Virginia.
    • (2001) Proc. American Control Conference , pp. 3013-3018
    • Hansson, A.1    Vandenberghe, L.2
  • 29
    • 0032072577 scopus 로고    scopus 로고
    • Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations
    • T. Iwasaki and S. Hara (1998). Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations. IEEE Trans. Aut. Control, AC-43(5):619-630.
    • (1998) IEEE Trans. Aut. Control , vol.AC-43 , Issue.5 , pp. 619-630
    • Iwasaki, T.1    Hara, S.2
  • 31
    • 0034857591 scopus 로고    scopus 로고
    • Fast algorithms for solving IQC feasibility and optimization problems
    • C.-Y. Kao and A. Megretski (2001). Fast algorithms for solving IQC feasibility and optimization problems. Proc. American Control Conf., 3019-3024.
    • (2001) Proc. American Control Conf , pp. 3019-3024
    • Kao, C.-Y.1    Megretski, A.2
  • 32
    • 0035309663 scopus 로고    scopus 로고
    • A cutting plane algorithm for robustness analysis of periodically time-varying systems
    • C.-Y. Kao, A. Megretski, and U. T. Jönsson (2001). A cutting plane algorithm for robustness analysis of periodically time-varying systems. IEEE Trans. Aut. Control, 46(4):579-592.
    • (2001) IEEE Trans. Aut. Control , vol.46 , Issue.4 , pp. 579-592
    • Kao, C.-Y.1    Megretski, A.2    Jönsson, U.T.3
  • 33
    • 33947501281 scopus 로고    scopus 로고
    • Specialized fast algorithms for IQC feasibility and optimization problems
    • Submitted for publication
    • C.-Y. Kao, A. Megretski, and U. Jönsson (2003). Specialized fast algorithms for IQC feasibility and optimization problems. Submitted for publication.
    • (2003)
    • Kao, C.-Y.1    Megretski, A.2    Jönsson, U.3
  • 34
    • 0022059319 scopus 로고    scopus 로고
    • J. Kautsky, N. K. Nichols, and P. Van Dooren (1985). Robust pole assignment in linear state feedback. Int. J. Control, 41:1129-1155.
    • J. Kautsky, N. K. Nichols, and P. Van Dooren (1985). Robust pole assignment in linear state feedback. Int. J. Control, 41:1129-1155.
  • 35
    • 33947537126 scopus 로고    scopus 로고
    • J. Löfberg (2002). YALMIP. Yet another LMI parser. University of Linköping, Sweden.
    • J. Löfberg (2002). YALMIP. Yet another LMI parser. University of Linköping, Sweden.
  • 36
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • S. Mehrotra (1991). On the implementation of a primal-dual interior point method. SIAM Journal on Optimization, 2(4):575-601.
    • (1991) SIAM Journal on Optimization , vol.2 , Issue.4 , pp. 575-601
    • Mehrotra, S.1
  • 37
    • 0031162465 scopus 로고    scopus 로고
    • System analysis via integral quadratic constraints
    • A. Megretski and A. Rantzer (1997). System analysis via integral quadratic constraints. IEEE Trans. Aut. Control, 42(6):819-830.
    • (1997) IEEE Trans. Aut. Control , vol.42 , Issue.6 , pp. 819-830
    • Megretski, A.1    Rantzer, A.2
  • 38
    • 33947494831 scopus 로고    scopus 로고
    • J. Oishi and V. Balakrishnan (1999). Linear controller design for the NEC laser bonder via LMI optimization. In Laurent El Ghaoui and Silviu-Iulian Niculescu (Editors). Advances in Linear Matrix Inequality Methods in Control. Advances in Control and Design. SIAM.
    • J. Oishi and V. Balakrishnan (1999). Linear controller design for the NEC laser bonder via LMI optimization. In Laurent El Ghaoui and Silviu-Iulian Niculescu (Editors). Advances in Linear Matrix Inequality Methods in Control. Advances in Control and Design. SIAM.
  • 39
    • 0028379059 scopus 로고
    • Gain scheduling via linear fractional transformations
    • A. Packard (1994). Gain scheduling via linear fractional transformations. Syst. Control Letters, 22:79-92.
    • (1994) Syst. Control Letters , vol.22 , pp. 79-92
    • Packard, A.1
  • 40
    • 33947507732 scopus 로고    scopus 로고
    • Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, Pasadena, California
    • P. A. Parrilo (2000). Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, Pasadena, California.
    • (2000)
    • Parrilo, P.A.1
  • 41
    • 0002676302 scopus 로고    scopus 로고
    • On the Kaiman-Yakubovich-Popov lemma
    • A. Rantzer (1996). On the Kaiman-Yakubovich-Popov lemma. Syst. Control Letters, 28(1):7-10.
    • (1996) Syst. Control Letters , vol.28 , Issue.1 , pp. 7-10
    • Rantzer, A.1
  • 42
    • 0020207749 scopus 로고
    • Stability margins of diagonally perturbed multivariable feedback systems
    • M. G. Safonov (1982). Stability margins of diagonally perturbed multivariable feedback systems. IEE Proc., 129-D:251-256.
    • (1982) IEE Proc , vol.129-D , pp. 251-256
    • Safonov, M.G.1
  • 43
    • 33947512060 scopus 로고    scopus 로고
    • 1.02, a Matlab Toolbox for Optimization Over Symmetric Cones. Available from
    • J. F. Sturm (2001). Using SEDUMI 1.02, a Matlab Toolbox for Optimization Over Symmetric Cones. Available from fewcal.kub.nl/sturm/software/sedumi.html.
    • (2001) Using SEDUMI
    • Sturm, J.F.1
  • 44
    • 0036923521 scopus 로고    scopus 로고
    • Implementation of interior point methods for mixed semidefinite and second order cone optimization problems
    • J. F. Sturm (2002). Implementation of interior point methods for mixed semidefinite and second order cone optimization problems. Optimization Methods and Software, 17(6):1105-1154.
    • (2002) Optimization Methods and Software , vol.17 , Issue.6 , pp. 1105-1154
    • Sturm, J.F.1
  • 45
    • 0032359979 scopus 로고    scopus 로고
    • On the Nesterov-Todd direction in semidefinite programming
    • M. J. Todd, K. C. Toh, and R. H. Tütüncü (1998). On the Nesterov-Todd direction in semidefinite programming. SIAM J. on Optimization, 8(3):769-796.
    • (1998) SIAM J. on Optimization , vol.8 , Issue.3 , pp. 769-796
    • Todd, M.J.1    Toh, K.C.2    Tütüncü, R.H.3
  • 46
    • 33947507314 scopus 로고    scopus 로고
    • K. C. Toh, R. H. Tütüncü, and M. J. Todd 2002, SDPT3 version 3.02. A Matlab software for semidefinite-quadratic-linear programming. Available from
    • K. C. Toh, R. H. Tütüncü, and M. J. Todd (2002). SDPT3 version 3.02. A Matlab software for semidefinite-quadratic-linear programming. Available from www.math.nus.edu.sg/~mattolikc/sdpt3.html.
  • 47
    • 0003857247 scopus 로고    scopus 로고
    • SDPSOL: A Parser/Solver for Semidefinite Programming and Determinant Maximization Problems with Matrix Structure
    • Stanford University
    • S.-P. Wu and S. Boyd (1996). SDPSOL: A Parser/Solver for Semidefinite Programming and Determinant Maximization Problems with Matrix Structure. User's Guide, Version Beta. Stanford University.
    • (1996) User's Guide, Version Beta
    • Wu, S.-P.1    Boyd, S.2
  • 48
    • 0036576194 scopus 로고    scopus 로고
    • Improved stability analysis and gainscheduled controller synthesis for parameter-dependent systems
    • F. Wang and V. Balakrishnan (2002). Improved stability analysis and gainscheduled controller synthesis for parameter-dependent systems. IEEE Trans. Aut. Control, 47(5):720-734.
    • (2002) IEEE Trans. Aut. Control , vol.47 , Issue.5 , pp. 720-734
    • Wang, F.1    Balakrishnan, V.2
  • 49
    • 0002453910 scopus 로고    scopus 로고
    • FIR filter design via spectral factorization and convex optimization
    • B. Datta Editor, Birkhauser
    • S.-P. Wu, S. Boyd, and L. Vandenberghe (1998). FIR filter design via spectral factorization and convex optimization. In B. Datta (Editor). Applied and Computational Control, Signals, and Circuits, 1:215-245, Birkhauser.
    • (1998) Applied and Computational Control, Signals, and Circuits , vol.1 , pp. 215-245
    • Wu, S.-P.1    Boyd, S.2    Vandenberghe, L.3
  • 51
    • 85064435790 scopus 로고    scopus 로고
    • Comparison of two structure-exploiting optimization algorithms for integral quadratic constraints
    • Milan, Italy
    • R. Wallin, H. Hansson, and L. Vandenberghe (2003). Comparison of two structure-exploiting optimization algorithms for integral quadratic constraints. Proc. IFAC Symposium on Robust Control Design, Milan, Italy.
    • (2003) Proc. IFAC Symposium on Robust Control Design
    • Wallin, R.1    Hansson, H.2    Vandenberghe, L.3
  • 52
    • 0015206454 scopus 로고
    • Least squares stationary optimal control and the algebraic Riccati equation
    • J. C. Willems (1971). Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Aut. Control, AC-16(6):621-634.
    • (1971) IEEE Trans. Aut. Control , vol.AC-16 , Issue.6 , pp. 621-634
    • Willems, J.C.1
  • 54
    • 0032081158 scopus 로고    scopus 로고
    • On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming
    • Y. Zhang (1998). On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming. SIAM J. on Optimization, 8:365-386.
    • (1998) SIAM J. on Optimization , vol.8 , pp. 365-386
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.