A Numerical Approach to the Estimation of the Solutions of some   Variational Problems with Convexity Costraints
  We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection problems within a Principal-Agent framework. Problems such as product lines design, optimal taxation, structured derivatives design, etc. can be studied through the scope of these models. We develop a method to estimate their optimal pricing schedules. 
Ivar Ekeland, Santiago Moreno