Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems
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机译:使用连续非线性松弛来解决约束最大熵采样问题
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摘要
We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem - the problem of choosing the s x s principal submatrix with maximal determinant from a given n x n positive definite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. A parallel implementation of the algorithm exhibits approximately linear speed-up for up to 8 processors, and has successfully solved problem instances that were heretofore intractable.
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机译:我们考虑约束最大熵采样问题的一个新的非线性松弛问题-受线性约束,从给定的n x n正定矩阵中选择具有最大行列式的s x s主子矩阵的问题。我们使用新的松弛方法针对该问题实现了分支定界算法。测试问题的性能远远优于以前的基于特征值松弛的实现。该算法的并行实现可实现多达8个处理器的近似线性加速,并成功解决了迄今为止难以解决的问题。
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