Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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A framework is given for building larger separable QCQPs from smaller ones with exact SDP relaxations by showing that exactness is preserved under separable horizontal connections through right-hand-side parameters, along with sufficient conditions for several classes of problems.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Separable QCQPs and Their Exact SDP Relaxations
A framework is given for building larger separable QCQPs from smaller ones with exact SDP relaxations by showing that exactness is preserved under separable horizontal connections through right-hand-side parameters, along with sufficient conditions for several classes of problems.