The following mathematical optimization program is non convex for $0\leq p<1$, and some convex function $f$:
$$\text{minimize}_x \|x\|^p_p+f(x)$$
I'm wondering if any one knows the state of the art method for solving this problem?
1-It is clear that we can apply a sub-gradient minimization (and reach to a local minimum), but I'm wondering if there are better approaches out there or not?
2-if there exist such approaches what's the theoretical reason that makes them better.
Thanks for your help!
By the way $\|x\|_p^p$ is defined as the following: $$\|x\|_p^p=\sum_i |x_i|^p$$
Look at this paper:
"IMPROVED ITERATIVELY REWEIGHTED LEAST SQUARES FOR UNCONSTRAINED SMOOTHED $\ell_q$ MINIMIZATION", By MING-JUN LAI , YANGYANG XU, AND WOTAO YIN
http://www.caam.rice.edu/~wy1/paperfiles/Rice_CAAM_TR11-12_Mtx_Rcvry_ncvx_Lq.PDF
I think it exactly refers to the same problem.
Update: The original link above is broken, but I found it again here:
https://www.math.ucla.edu/~wotaoyin/papers/pdf/Rice_CAAM_TR11-12_Mtx_Rcvry_ncvx_Lq.pdf