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Polynomial Optimization on Some Unbounded Closed Semi-algebraic Sets

Author

Listed:
  • Trang T. Du

    (University of Transport and Communications)

  • Toan M. Ho

    (VAST)

Abstract

The article presents a study on a class of polynomial optimization problems over (noncompact) semi-algebraic sets which, by making changes of variables via suitable monomial mappings, become polynomial optimization problems over compact semi-algebraic feasible sets. It is known that the polynomial optimization problems on semi-algebraic feasible sets are satisfactory when the feasible sets are compact. Furthermore, determining whether a polynomial is bounded on such a semi-algebraic set can be replaced by checking whether its support lies in a closed and convex cone corresponding to the semi-algebraic set.

Suggested Citation

  • Trang T. Du & Toan M. Ho, 2019. "Polynomial Optimization on Some Unbounded Closed Semi-algebraic Sets," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 352-363, October.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01544-5
    DOI: 10.1007/s10957-019-01544-5
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    References listed on IDEAS

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    1. V. Jeyakumar & J. B. Lasserre & G. Li, 2014. "On Polynomial Optimization Over Non-compact Semi-algebraic Sets," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 707-718, December.
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