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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

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01242047/
Date
2017
Journal name
Applied Mathematics and Optimization
Volume
76
Number
3
Publisher
Springer
Pages
565-592
Publication identifier
10.1007/s00245-016-9361-5
Metadata
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Author(s)
Carlier, Guillaume
Dupuis, Xavier cc
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 [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.
Subjects / Keywords
Principal-agent problem; b-convexity constraint; convexity constraint; convex envelopes; iterated projections; Dykstra’s algorithm

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