Testing copositivity with the help of difference-of-convex optimization |
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Authors: | Mirjam Dür Jean-Baptiste Hiriart-Urruty |
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Institution: | 1. Department of Mathematics, University of Trier, 54286, Trier, Germany 2. Institut de Mathématiques, Université Paul Sabatier (Toulouse III), 118, route de Narbonne, 31062, Toulouse Cedex 9, France
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Abstract: | We consider the problem of minimizing an indefinite quadratic form over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective critical points and minima. We then apply a subgradient algorithm to approximate those critical points and obtain an efficient heuristic to verify non-copositivity of a matrix. |
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