We develop a novel optimization model to maximize the pro€t of a Demand-Side Platform (DSP) while ensuring that the budget utilization preferences of the DSP’s advertiser clients are adequately met. Our model is highly ƒexible and can be applied in a RealTime Bidding environment (RTB) with arbitrary auction types, e.g., both €rst and second price auctions. Our proposed formulation leads to a non-convex optimization problem due to the joint optimization over both impression allocation and bid price decisions. Using Fenchel duality theory, we construct a dual problem that is convex and can be solved eciently to obtain feasible bidding prices and allocation variables that can be deployed in a RTB seŠing. With a few minimal additional assumptions on the properties of the auctions, we demonstrate theoretically that our computationally ecient procedure based on convex optimization principles is guaranteed to deliver a globally optimal solution. We conduct experiments using data from a real DSP to validate our theoretical €ndings and to demonstrate that our method successfully trades o‚ between DSP pro€tability and budget utilization in a simulated online environment.