Polynomial Optimization on Some Unbounded Closed Semi-algebraic Sets

Trang T. Du () and Toan M. Ho ()
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Trang T. Du: University of Transport and Communications
Toan M. Ho: VAST

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 18, 352-363

Abstract: 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.

Keywords: Sum of squares; Positivstellensatz; Polynomial optimization; 90C30; 14P10; 49K99 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01544-5

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