The l2,0-regularized factored least-squares objective and its DC surrogates satisfy the KL property of exponent 1/2 at global minimizers under a near-isometry condition on the sampling operator.
A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements
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abstract
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random measurements of a positive semidefinite $n \times n$ matrix of rank $r$ and condition number $\kappa$, our method is guaranteed to converge linearly to the global optimum.
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KL property of exponent $1/2$ of $\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery
The l2,0-regularized factored least-squares objective and its DC surrogates satisfy the KL property of exponent 1/2 at global minimizers under a near-isometry condition on the sampling operator.