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Computable representation of the cone of nonnegative quadratic forms over a general second-order cone and its application to completely positive programming

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  • In this paper, we provide a computable representation of the cone of nonnegative quadratic forms over a general nontrivial second-order cone using linear matrix inequalities (LMI). By constructing a sequence of such computable cones over a union of second-order cones, an efficient algorithm is designed to find an approximate solution to a completely positive programming problem using semidefinite programming techniques. In order to accelerate the convergence of the approximation sequence, an adaptive scheme is adopted, and ``reformulation-linearization technique'' (RLT) constraints are added to further improve its efficiency.
    Mathematics Subject Classification: Primary: 90C26, 90C59, 90C22; Secondary: 30E10.


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