An iterated projection approach to variational problems under generalized convexity constraints
Carlier, Guillaume; Dupuis, Xavier (2017), An iterated projection approach to variational problems under generalized convexity constraints, Applied Mathematics and Optimization, 76, 3, p. 565-592. 10.1007/s00245-016-9361-5
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01242047/
Journal nameApplied Mathematics and Optimization
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Abstract (EN)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  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 . Our method also turns out to be simple for convex envelope computations.
Subjects / KeywordsPrincipal-agent problem; b-convexity constraint; convexity constraint; convex envelopes; iterated projections; Dykstra’s algorithm
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