1. A method for encoding video information, the method comprising: determining a first Lagrangian multiplier with a video encoder, wherein determining the first Lagrangian multiplier comprises estimating the first Lagrangian multiplier by using at least global information, the estimation of the first Lagrangian multiplier comprising calculating λ estimate , wherein λ estimate is a function of a global estimation method ƒ global (·) for global information I global , wherein λ estimate =ƒ global (I global ), and wherein the global information comprises a frame rate, or a current coding structure, or a hierarchy level within a current Group of Pictures (GOP); initializing a second Lagrangian multiplier; and updating the second Lagrangian multiplier with the first Lagrangian multiplier, wherein the updated second Lagrangian multiplier is a function of the first Lagrangian multiplier and the current second Lagrangian multiplier; wherein the video encoder encodes video information according to the updated second Lagrangian multiplier.