A rate control technique for video encoding under complex transmission scenarios is presented. A typical application for this method is the transmission of video over variable bit rate channels while accounting for restrictions on the end-to-end delay and decoder buffer size. That the resulting multiple constraints on the source and channel rates may be relaxed without loss of optimality into a set of linear inequality constraints-though they are usually expressed in nonlinear form-is a key insight of this paper. This allows for a systematic treatment of a large class of rate constraints and leads to a convex programming (CP) formulation for rate control. Approximation of the frame distortion-rate data by piecewise linear functions further facilitates an efficient solution based on linear programming (LP), a special case of CP. The LP method provides bounds for the deviation from optimality. Results for a standard video test set show that the proposed method provides solutions with mean square error (MSE) distortion value within 2% of the global minimum across a range of rates. The proposed technique is also applied in conjunction with a perceived distortion measure. Results exhibit significant reduction in blocking artifacts and flicker compared to the use of MSE