Extension of Eaves Theorem for Determining the Boundedness of Convex Quadratic Programming Problems

It is known that the boundedness of a convex quadratic function over a convex quadratic constraint (c-QP) can be determined by algorithms. In 1985, Terlaky transformed the said boundedness problem into an lp programming problem and then apply linear programming, while Caron and Obuchowska in 1995 pr...

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Published inTaiwanese journal of mathematics Vol. 24; no. 6; pp. 1551 - 1563
Main Authors Nguyen, Huu-Quang, Nguyen, Van-Bong, Sheu, Ruey-Lin
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2020
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Summary:It is known that the boundedness of a convex quadratic function over a convex quadratic constraint (c-QP) can be determined by algorithms. In 1985, Terlaky transformed the said boundedness problem into an lp programming problem and then apply linear programming, while Caron and Obuchowska in 1995 proposed another iterative procedure that checks, repeatedly, the existence of the implicit equality constraints. Theoretical characterization about the boundedness of (c-QP), however, does not have a complete result so far, except for Eaves' theorem, first by Eaves and later by Dostál, which answered the boundedness question only partially for a polyhedral-type of constraints. In this paper, Eaves' theorem is generalized to answer, necessarily and sufficiently, when the general (c-QP) with a convex quadratic constraint (not just a polyhedron) can be bounded from below, with a new insight that it can only be unbounded within an affine subspace.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/200501