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Optimal solution approximation for infinite positive-definite quadratic programming

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Abstract

We consider a general doubly-infinite, positive-definite, quadratic programming problem. We show that the sequence of unique optimal solutions to the natural finite-dimensional subproblems strongly converges to the unique optimal solution. This offers the opportunity to arbitrarily well approximate the infinite-dimensional optimal solution by numerically solving a sufficiently large finite-dimensional version of the problem. We then apply our results to a general time-varying, infinite-horizon, positive-definite, LQ control problem.

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References

  1. Lewis, F. L.,Optimal Control, Wiley, New York, New York, 1986.

    Google Scholar 

  2. Lee, K. Y., Chow, S., andBarr, R. O.,On the Control of Discrete-Time Distributed Parameter Systems, SIAM Journal on Control, Vol. 10, pp. 361–376, 1972.

    Google Scholar 

  3. Zabczyk, J.,Remarks on the Control of Discrete-Time Distributed Parameter Systems, SIAM Journal on Control, Vol. 12, pp. 721–773, 1974.

    Google Scholar 

  4. Milne, R. D.,Applied Functional Analysis, Pitman, Boston, Massachusetts, 1980.

    Google Scholar 

  5. Aubin, J. P.,Applied Functional Analysis, Wiley, New York, New York, 1979.

    Google Scholar 

  6. Schochetman, I. E., andSmith, R. L.,Solution Approximation in Infinite-Horizon Linear Quadratic Control, IEEE Transactions on Automatic Control, Vol. 39, pp. 596–601, 1994.

    Google Scholar 

  7. Dunford, N., andSchwartz, J. T.,Linear Operators, Vol. 1, Wiley-Interscience, New York, New York, 1964.

    Google Scholar 

  8. Kolmogorov, A. N., andFomin, S. V.,Introductory Real Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1970.

    Google Scholar 

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Authors and Affiliations

  1. Rubicon, Ann Arbor, Michigan

    P. Benson (President)

  2. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan

    R. L. Smith (Professor)

  3. Department of Mathematical Sciences, Oakland University, Rochester, Michigan

    I. E. Schochetman (Professor)

  4. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan

    J. C. Bean (Professor)

Authors
  1. P. Benson
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  2. R. L. Smith
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  3. I. E. Schochetman
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  4. J. C. Bean
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Additional information

Communicated by D. G. Luenberger

This work was supported in part by the National Science Foundation under Grants ECS-8700836, DDM-9202849, and DDM-9214894.

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Benson, P., Smith, R.L., Schochetman, I.E. et al. Optimal solution approximation for infinite positive-definite quadratic programming. J Optim Theory Appl 85, 235–248 (1995). https://doi.org/10.1007/BF02192225

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  • DOI: https://doi.org/10.1007/BF02192225

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