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.

An iterated projection approach to variational problems under generalized convexity constraints / Carlier, Guillaume; Dupuis, Xavier. - (2015).

An iterated projection approach to variational problems under generalized convexity constraints

DUPUIS, XAVIER
2015

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.
Principal-agent problem, b-convexity constraint, convexity constraint, convex envelopes, iterated projections, Dykstra's algorithm
An iterated projection approach to variational problems under generalized convexity constraints / Carlier, Guillaume; Dupuis, Xavier. - (2015).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/160726
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