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December, 2020 Extension of Eaves Theorem for Determining the Boundedness of Convex Quadratic Programming Problems
Huu-Quang Nguyen, Van-Bong Nguyen, Ruey-Lin Sheu
Taiwanese J. Math. 24(6): 1551-1563 (December, 2020). DOI: 10.11650/tjm/200501


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 $l_p$ 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.


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Huu-Quang Nguyen. Van-Bong Nguyen. Ruey-Lin Sheu. "Extension of Eaves Theorem for Determining the Boundedness of Convex Quadratic Programming Problems." Taiwanese J. Math. 24 (6) 1551 - 1563, December, 2020.


Received: 24 July 2019; Revised: 12 January 2020; Accepted: 3 May 2020; Published: December, 2020
First available in Project Euclid: 19 November 2020

MathSciNet: MR4176886
Digital Object Identifier: 10.11650/tjm/200501

Primary: 90C20 , 90C22 , 90C32

Keywords: $l_p$ programming , convex quadratic programming , Eaves theorem , recession cone

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 6 • December, 2020
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