Applications of Constrained Optimization


Constrained optimization provides a general framework in which a variety of design criteria and specifications can be readily imposed on the required solution. Usually, a multivariable objective function that quantifies a performance measure of a design can be identified. This objective function may be linear, quadratic, or highly nonlinear, and usually it is differentiable so that its gradient and sometimes Hessian can be evaluated. In a real-life design problem, the design is carried out under certain physical limitations with limited resources. If these limitations can be quantified as equality or inequality constraints on the design variables, then a constrained optimization problem can be formulated whose solution leads to an optimal design that satisfies the limitations imposed. Depending on the degree of nonlinearity of the objective function and constraints, the problem at hand can be a linear programming (LP), quadratic programming (QP), convex programming (CP), semidefinite programming (SDP), second-order cone programming (SOCP), or general nonlinear constrained optimization problem.


Contact Force Model Predictive Control Multiuser Detector Robot Hand Dextrous Hand 
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  1. 1.
    A. Antoniou, Digital Singal Processing: Signals, Systems, and Filters, McGraw-Hill, New York, 2005.Google Scholar
  2. 2.
    W.-S. Lu and A. Antoniou, Two-Dimensional Digital Filters, Marcel Dekker, New York, 1992.MATHGoogle Scholar
  3. 3.
    J. W. Adams, “FIR digital filters with least-squares stopbands subject to peak-gain constraints,” IEEE Trans. Circuits Syst., vol. 38, pp. 376–388, April 1991.CrossRefGoogle Scholar
  4. 4.
    W.-S. Lu, “Design of nonlinear-phase FIR digital filters: A semidefinite programming approach,” IEEE Int. Symp. on Circuits and Systems, vol. III, pp. 263–266, Orlando, FL., May 1999.Google Scholar
  5. 5.
    A. G. Deczky, “Synthesis of recursive digital filters using the minimum p-error criterion,” IEEE Trans. Audio and Electroacoustics, vol. 20, pp. 257–263, 1972.CrossRefGoogle Scholar
  6. 6.
    A. T. Chottra and G. A. Jullien, “A linear programming approach to recursive digital filter design with linear phase,” IEEE Trans. Circuits Syst., vol. 29, pp. 139–149, Mar. 1982.CrossRefGoogle Scholar
  7. 7.
    W.-S. Lu, S.-C. Pei, and C.-C. Tseng, “A weighted least-squares method for the design of stable 1-D and 2-D IIR filters,” IEEE Trans. Signal Processing, vol. 46, pp. 1–10, Jan. 1998.CrossRefGoogle Scholar
  8. 8.
    M. Lang, “Weighted least squares IIR filter design with arbitrary magnitude and phase responses and specified stability margin,” IEEE Symp. on Advances in Digital Filtering and Signal Processing, pp. 82–86, Victoria, BC, June 1998.Google Scholar
  9. 9.
    T. Kailath, Linear Systems, Englewood Cliffs, Prentice-Hall, NJ., 1981.Google Scholar
  10. 10.
    C. E. Garcia, D. M. Prett, and M. Morari, “Model predictive control: Theory and practice — a survey,” Automatica, vol. 25, pp. 335–348, 1989.MATHCrossRefGoogle Scholar
  11. 11.
    M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, pp. 1361–1379, 1996.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, Wiley, New York, 1972.MATHGoogle Scholar
  13. 13.
    J. Kerr and B. Roth, “Analysis of multifingered hands,” Int. J. Robotics Research, vol. 4, no. 4, pp. 3–17, Winter 1986.CrossRefGoogle Scholar
  14. 14.
    D. E. Orin and F.-T. Cheng, “General dynamic formulation of the force distribution equations,” Proc. 4th Int. Conf. on Advanced Robotics, pp. 525–546, Columbus, Ohio, June 13–15, 1989.Google Scholar
  15. 15.
    F.-T. Cheng and D. E. Orin, “Efficient algorithm for optimal force distribution — The compact-dual LP method,” IEEE Trans. Robotics and Automation, vol. 6, pp. 178–187, April 1990.CrossRefGoogle Scholar
  16. 16.
    E. S. Venkaraman and T. Iberall, Dextrous Robot Hands, Springer Verlag, New York, 1990.Google Scholar
  17. 17.
    M. Buss, H. Hashimoto, and J. B. Moore, “Dextrous hand grasping force optimization,” IEEE Trans. Robotics and Automation, vol. 12, pp. 406–418, June 1996.CrossRefGoogle Scholar
  18. 18.
    K. Shimoga, “Robot grasp synthesis algorithms: Asurvey,” Int. J. Robotics Research, vol. 15, pp. 230–266, June 1996.CrossRefGoogle Scholar
  19. 19.
    J. G. Proakis, Digial Communications, 3rd ed., McGraw-Hill, New York, 1995.Google Scholar
  20. 20.
    S. Verdú, Multiuser Detection, Cambridge University Press, New York, 1998.MATHGoogle Scholar
  21. 21.
    S. Verdú, “Minimum probability of error for asynchronous Gaussian multiple-access channels,” IEEE Trans. Inform. Theory, vol. 32, pp. 85–96, Jan. 1986.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    X. M. Wang, W.-S. Lu, and A. Antoniou, “A near-optimal multiuser detector for CDMA channels using semidefinite programming relaxation,” Proc. Int. Symp. Circuits Syst., Sydney, Australia, June 2001.Google Scholar
  23. 23.
    X. F. Wang, W.-S. Lu, and A. Antoniou, “Constrained minimum-BER multiuser detection,” IEEE Trans. Signal Processing, vol. 48, pp. 2903–2909, Oct. 2000.CrossRefGoogle Scholar
  24. 24.
    M. X. Geomans and D. P. Williamson, “Improved approximation algorithms for maximum cut and satisfiability problem using semidefinite programming,” J. ACM, vol. 42, pp. 1115–1145, 1995.CrossRefGoogle Scholar
  25. 25.
    M. X. Geomans and D. P. Williamson, “.878-approximation algorithm for MAX-CUT and MAX-2SAT,” Proc. 26th ACM Symp. Theory of Computing, pp. 422–431, 1994.Google Scholar
  26. 26.
    L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Review, vol. 38, pp. 49–95, 1996.MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook on Semidefinite Programming, Kluwer Academic, MA, 2000.Google Scholar
  28. 28.
    G. W. Stewart, Introduction to Matrix Computations, New York, Academic Press, 1973.MATHGoogle Scholar
  29. 29.
    K. C. Toh, R. H. Tütüncü, and M. J. Todd, “On the implementation of SDPT3 version 3.1 — a MATLAB software package for semidefinite-quadratic-linear Programming,” Proc. IEEE Conf. on Computer-Aided Control System Design, Sept. 2004.Google Scholar
  30. 30.
    A. Nemirovski and P. Gahinet, “The projective method for solving linear matrix inequalities,” Math. Programming, Series B, vol. 77, pp. 163–190, 1997.MathSciNetGoogle Scholar
  31. 31.
    P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, Manual of LMI Control Toolbox, Natick: Math Works Inc., May 1990.Google Scholar

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