Error bound of critical points and KL property of exponent $1/2$ for squared F-norm regularized factorization

no code implementations • 11 Nov 2019 • Ting Tao, Shaohua Pan, Shujun Bi

This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems.

KL property of exponent $1/2$ of $\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery

no code implementations • 24 Aug 2019 • Shujun Bi, Ting Tao, Shaohua Pan

To cater for the scenario in which only a coarse estimation is available for the rank of the true matrix, an $\ell_{2, 0}$-norm regularized term is added to the factored loss function to reduce the rank adaptively; and account for the ambiguities in the factorization, a balanced term is then introduced.

Equivalent Lipschitz surrogates for zero-norm and rank optimization problems

no code implementations • 30 Apr 2018 • Yulan Liu, Shujun Bi, Shaohua Pan

Specifically, we reformulate these combinatorial problems as equivalent MPECs by the variational characterization of the zero-norm and rank function, show that their penalized problems, yielded by moving the equilibrium constraint into the objective, are the global exact penalization, and obtain the equivalent Lipschitz surrogates by eliminating the dual variable in the global exact penalty.