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- W2122438533 abstract "A symmetric matrix is called copositive if it generates a quadratic form taking no negative values over the nonnegative orthant, and the linear optimization problem over the set of copositive matrices is called the copositive programming problem. Recently, many studies have been done on the copositive programming problem (see, for example, (14, 5)). Among others, several branch and bound type algorithms have been provided to test copositivity in the context of the fact that deciding whether a given matrix is copositive is co-NP-complete (23, 13). In this paper, we propose a new branch and bound type algorithm for this testing problem based on Sponsel, Bundfuss and Dur's algorithm (27). Two features of our algorithm are: (1) we introduce new classes of matrices G s n and ! G s n which are relatively large subsets of the set of copositive matrices and work well to check copositivity of a givenn!nsymmetric matrix, and (2) for incorporating the setsG s n or ! s n in checking copositivity, we only have to solve a linear optimization problem withn+ 1 variables andO(n 2 ) constraints after computing a singular value matrix decomposition, which implies that our algorithm is not so time-consuming. Our preliminary numerical experiments suggest that our algorithm is promising for determining upper bounds of the maximum clique problem." @default.
- W2122438533 created "2016-06-24" @default.
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- W2122438533 date "2014-05-01" @default.
- W2122438533 modified "2023-09-27" @default.
- W2122438533 title "An LP-based Algorithm to Test Copositivity" @default.
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