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Michael Orlitzky (michaelorlitzky.com) Abstract: A real symmetric matrix "A" is copositive if the inner product if Ax and x is nonnegative for all x in the nonnegative orthant. Copositive programming has attracted a lot of attention since Burer showed that hard nonconvex problems can be formulated as completelypositive programs. Alas, the power of copositive programming is offset by its difficulty: simple questions like "is this matrix copositive?" have complicated answers. In 1958, Jerry Gaddum proposed a recursive procedure to check if a given matrix is copositive by solving a series of matrix games. It is easy to implement and conceptually simple. Copositivity generalizes to cones other than the nonnegative orthant. If K is a proper cone, then the linear operator L is copositive on K if the inner product of L(x) and x is nonnegative for all x in K. Little is known about these operators in general. We extend Gaddum's test to selfdual and symmetric cones, thereby deducing criteria for copositivity in those settings. Keywords: copositivity, copositive programming, linear games, conic optimization, Euclidean Jordan algebra Category 1: Linear, Cone and Semidefinite Programming Category 2: Complementarity and Variational Inequalities Category 3: Other Topics (Game Theory ) Citation: Journal of Global Optimization (2020) https://link.springer.com/article/10.1007%2Fs10898020009606 Download: Entry Submitted: 12/16/2019 Modify/Update this entry  
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