\input zb-basic
\input zb-ioport
\iteman{io-port 06081313}
\itemau{Peng, Zhen-Yun; Wang, Lin; Peng, Jing-Jing}
\itemti{The solutions of matrix equation $AX=B$ over a matrix inequality constraint.}
\itemso{SIAM J. Matrix Anal. Appl. 33, No. 2, 554-568 (2012).}
\itemab
The authors consider Problem I: Find $X$ such that $AX = B$ with matrix inequality constraint $CXD \geq E$ for properly dimensioned matrices. An iterative method is proposed to solve the smallest nonnegative deviation of a matrix inequality. Based on the results obtained from this iterative method and some existing known results on matrix equations, they obtain consistent conditions and general expressions for the solutions to Problem I. Compared with the augmented Lagrangian and the predictor-corrector interior point methods (with necessary modifications to be applicable to Problem I), their algorithm is shown to be numerically efficient.
\itemrv{R\'emi Vaillancourt (Ottawa)}
\itemcc{}
\itemut{matrix equation; matrix inequality; iterative method; nonnegative matrix; predictor-corrector interior point methods; algorithm}
\itemli{doi:10.1137/100808678}
\end