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We present an algorithm to approximate the solutions to variational problemswhere set of admissible functions consists of convex functions. The mainmotivator behind this numerical method is estimating solutions to AdverseSelection problems within a Principal-Agent framework. Problems such as productlines design, optimal taxation, structured derivatives design, etc. can bestudied through the scope of these models. We develop a method to estimatetheir optimal pricing schedules.

A Numerical Approach to the Estimation of the Solutions of some Variational Problems with Convexity Costraints