  The best pair problem aims to find a pair of points that minimize the
distance between two disjoint sets. In this paper, we formulate the classical
robust principal component analysis (RPCA) as the best pair; which was not
considered before. We design an accelerated proximal gradient scheme to solve
it, for which we show global convergence, as well as the local linear rate. Our
extensive numerical experiments on both real and synthetic data suggest that
the algorithm outperforms relevant baseline algorithms in the literature.
