We develop a novel optimization model to maximize the profit of a Demand-Side Platform (DSP) while ensuring that the budget utilization preferences of the DSPs advertiser clients are adequately met. Our model is highly flexible and can be applied in a Real-Time Bidding environment (RTB) with arbitrary auction types, e.g., both first 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 efficiently to obtain feasible bidding prices and allocation variables that can be deployed in a RTB setting. With a few minimal additional assumptions on the properties of the auctions, we demonstrate theoretically that our computationally efficient 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 findings and to demonstrate that our method successfully trades off between DSP profitability and budget utilization in a simulated online environment.
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