Journal of Optimization Theory and Applications

, Volume 33, Issue 2, pp 207–221

Solving nonlinear inequalities in a finite number of iterations

  • D. Q. Mayne
  • E. Polak
  • A. J. Heunis
Contributed Papers

Abstract

This paper describes a modified Newton algorithm for solving a finite system of inequalities in a finite number of iterations.

Key Words

Inequality constraints feasible point algorithms finite convergence 

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References

  1. 1.
    Polak, E.,Computational Methods in Optimization, Academic Press, New York, New York, 1971.Google Scholar
  2. 2.
    Zakian, N., andAl-naib, U.,Design of Dynamical and Control Systems by the Method of Inequalities, Proceedings of the Institution of Electrical and Electronic Engineers, Vol. 120, pp. 1421–1472, 1973.Google Scholar
  3. 3.
    Becker, R. G., Heunis, A. J., andMayne, D. Q.,Computer Aided Design via Optimization, Imperial College, London, England, Department of Computing and Control, Research Report No. 78/47, 1978.Google Scholar
  4. 4.
    Polak, E., andMayne, D. Q.,On the Finite Solution of Nonlinear Inequalities, University of California, Berkeley, California, Electronics Research Laboratory, Memorandum No. UCB/ERL-M78/80, 1978.Google Scholar
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    Daniel, J. W.,On Perturbations in Systems of Linear Inequalities, SIAM Journal on Numerical Analysis, Vol. 10, pp. 299–303, 1973.Google Scholar
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    Powell, M. J. D.,Variable Metric Methods for Constrained Optimization, Paper Presented at the 3rd International Symposium on Computing Methods in Applied Science and Engineering, Paris, France, 1977.Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • D. Q. Mayne
    • 2
  • E. Polak
    • 1
  • A. J. Heunis
    • 2
  1. 1.Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of CaliforniaBerkeley
  2. 2.Computer Aided Design Group, Department of Computing and ControlImperial College of Science and TechnologyLondonEngland

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