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

Huu Quang Nguyen, Van Bong Nguyen, Ruey Lin Sheu

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1551-1563
Number of pages13
JournalTaiwanese Journal of Mathematics
Volume24
Issue number6
DOIs
Publication statusPublished - 2020 Dec

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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