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Solving nonlinear inequalities in a finite number of iterations

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Abstract

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

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References

  1. Polak, E.,Computational Methods in Optimization, Academic Press, New York, New York, 1971.

    Google Scholar 

  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. 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.

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  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 

  5. Daniel, J. W.,On Perturbations in Systems of Linear Inequalities, SIAM Journal on Numerical Analysis, Vol. 10, pp. 299–303, 1973.

    Google Scholar 

  6. 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.

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Communicated by Y. C. Ho

This research was supported by NSF Grant No. ENG-73-08214-AO1, by NSF-RANN Grant No. ENV-76-04264, and by the United Kingdom Science Research Council.

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Mayne, D.Q., Polak, E. & Heunis, A.J. Solving nonlinear inequalities in a finite number of iterations. J Optim Theory Appl 33, 207–221 (1981). https://doi.org/10.1007/BF00935547

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