Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 23, Issue 1, Pages 432-451Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110826862
Keywords
trust-region subproblem; second-order-cone programming; semidefinite programming; nonconvex quadratic programming
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Funding
- NSF grant [CCF-0545514]
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The classical trust-region subproblem (TRS) minimizes a nonconvex quadratic objective over the unit ball. In this paper, we consider extensions of TRS having extra constraints. When two parallel cuts are added to TRS, we show that the resulting nonconvex problem has an exact representation as a semidefinite program with additional linear and second-order-cone (SOC) constraints. For the case where an additional ellipsoidal constraint is added to TRS, resulting in the two trust-region subproblem (TTRS), we provide a new relaxation including SOC constraints that strengthens the usual semidefinite programming (SDP) relaxation.
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