The penetration of renewables and demand-response programs will inevitably lead to frequent flow reversals and substation reconfigurations, while high-throughput synchrophasor measurement units are being installed throughout the grid. Hence, jointly verifying circuit breaker statuses and estimating the state of power networks of increasing dimensionality becomes even more challenging. Building on generalized state estimation, revisited in the light of modern measurement capabilities, the aforementioned task is relaxed to a convex optimization problem. Exploiting compressive sampling advances, the prior information on unmonitored and suspected switches takes the form of ℓ2-norm penalties promoting sparsity in a properly defined block manner. An efficient algorithm is developed to ensure compatibility with solvers found currently at control centers. Numerical tests on the IEEE 14-bus model corroborate the effectiveness of the novel scheme.