This paper considers coordinated linear precoding for rate optimization in downlink multicell, multiuser orthogonal frequency- division multiple access networks. We focus on two different design criteria. In the first, the weighted sum-rate is maximized under transmit power constraints per base station. In the second, we minimize the total transmit power satisfying the signal-to-interference-plus-noise-ratio constraints of the subcarriers per cell. Both problems are solved using standard conic optimization packages. A less complex, fast, and provably convergent algorithm that maximizes the weighted sum-rate with per-cell transmit power constraints is formulated. We approximate the nonconvex weighted sum- rate maximization (WSRM) problem with a solvable convex form by means of a sequential parametric convex approximation approach. The second- order cone formulations of an objective function and the constraints of the optimization problem are derived through a proper change of variables, first-order linear approximation, and hyperbolic constraints transformation. This algorithm converges to the suboptimal solution while taking fewer it- erations in comparison to other known iterative WSRM algorithms. Numerical results are presented to demonstrate the effectiveness and superiority of the proposed algorithm.