An iterated projection approach to variational problems under generalized convexity constraints

Abstract : The principal-agent problem in economics leads to variational problems subject to global constraints of b-convexity on the admissible functions, capturing the so-called incentive-compatibility constraints. Typical examples are minimization problems subject to a convexity constraint. In a recent pathbreaking article, Fi-galli, Kim and McCann [19] identified conditions which ensure convexity of the principal-agent problem and thus raised hope on the development of numerical methods. We consider special instances of projections problems over b-convex functions and show how they can be solved numerically using Dykstra's iterated projection algorithm to handle the b-convexity constraint in the framework of [19]. Our method also turns out to be simple for convex envelope computations.
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Submitted on : Friday, December 11, 2015 - 1:29:04 PM
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Guillaume Carlier, Xavier Dupuis. An iterated projection approach to variational problems under generalized convexity constraints. 2015. ⟨hal-01242047⟩

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