We consider sparse array beamfomer design achieving maximum signal-to interference plus noise ratio (MaxSINR). Both array configuration and weights are attuned to the changing sensing environment. This is accomplished by simultaneously switching among antenna positions and adjusting the corresponding weights. The sparse array optimization design requires estimating the data autocorrelations at all spatial lags across the array aperture. Towards this end, we adopt low rank matrix completion under the semidefinite Toeplitz constraint for interpolating those autocorrelation values corresponding to the missing lags. We compare the performance of matrix completion approach with that of the fully augmentable sparse array design acting on the same objective function. The optimization tool employed is the regularized $l_1$-norm successive convex approximation (SCA). Design examples with simulated data are presented using different operating scenarios, along with performance comparisons among various configurations.