Two Relaxation Methods for Rank Minimization Problems
Two Relaxation Methods for Rank Minimization Problems
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DOI：
10.1007/s10957-020-01731-9
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发表时间：
2020-08
影响因子：
1.9
通讯作者：
April Sagan;Xin Shen;J. Mitchell
中科院分区：
文献类型：
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作者：
April Sagan;Xin Shen;J. Mitchell
将约束条件下对称半正定矩阵的秩最小化问题提升为一个等价的带互补约束的半定规划问题。该公式要求两个半正定矩阵是互补的。这是一个连续的和非凸的重新制定的秩最小化问题。我们开发了两个松弛，并表明约束资格持有在任何驻点的秩最小化问题的任何松弛，我们探索的局部极小的结构。
The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be lifted to give an equivalent semidefinite program with complementarity constraints. The formulation requires two positive semidefinite matrices to be complementary. This is a continuous and nonconvex reformulation of the rank minimization problem. We develop two relaxations and show that constraint qualification holds at any stationary point of either relaxation of the rank minimization problem, and we explore the structure of the local minimizers.