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Quadratic optimization over a polyhedral cone

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  • In this paper, we study the polyhedral cone constrained homogeneous quadratic programming problem and provide an equivalent linear conic reformulation. Based on a union of second-order cones which covers the polyhedral cone, a sequence of computable linear conic programming problems are constructed to approximate the linear conic reformulation. The convergence of the sequential solutions is guaranteed as the number of second-order cones increases such that the union of the second-order cones gets close to the polyhedral cone. In order to relieve the computational burden and improve the efficiency, an adaptive scheme and valid inequalities derived by the reformulation-linearization technique are added to the proposed algorithm. Finally, the numerical results demonstrate the effectiveness of the algorithm.
    Mathematics Subject Classification: Primary: 90C26, 90C59, 90C22; Secondary: 30E10.


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