Extension of eaves theorem for determining the boundedness of convex quadratic programming problems

Huu Quang Nguyen, Van Bong Nguyen, Ruey Lin Sheu

研究成果: Article同行評審

摘要

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 con-straints. 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.

原文English
頁(從 - 到)1551-1563
頁數13
期刊Taiwanese Journal of Mathematics
24
發行號6
DOIs
出版狀態Published - 2020 十二月

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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