科研之友
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摘要
In this paper, we prove that detecting the copositivity of a given matrix over a p-th order cone is equivalent to the decision problem of a quadratic programming problem over a cross-section of the p-th order cone. Then we identify some polynomial-time solvable subclasses for the detection problem. Based on the linear matrix inequality representations of the cone of nonnegative quadratic forms over a union of second order cones, a conic approximation algorithm is presented for the problems not belonging to the polynomial-time solvable subclasses. Computational experiments are conducted to illustrate the efficiency of the proposed algorithm.
