An iterative support shrinking algorithm for $\ell_{p}$-$\ell_{q}$ minimization
This work addresses the need for efficient and theoretically grounded algorithms for nonconvex ℓp-ℓq minimization, which is relevant for sparse signal recovery and compressed sensing.
The authors propose an iterative support shrinking algorithm for ℓp-ℓq minimization (0<p<1≤q<∞) that guarantees nonexpansiveness of the signal support set and converges globally to a stationary point. They also provide a practical lower bound theory for the iteration sequence.
We present an iterative support shrinking algorithm for $\ell_{p}$-$\ell_{q}$ minimization~($0 <p < 1 \leq q < \infty $). This algorithm guarantees the nonexpensiveness of the signal support set and can be easily implemented after being proximally linearized. The subproblem can be very efficiently solved due to its convexity and reducing size along iteration. We prove that the iterates of the algorithm globally converge to a stationary point of the $\ell_{p}$-$\ell_{q}$ objective function. In addition, we show a lower bound theory for the iteration sequence, which is more practical than the lower bound results for local minimizers in the literature.