A Primal-Dual Partial Inverse Algorithm for Constrained Monotone Inclusions: Applications to Stochastic Programming and Mean Field Games

In this work, we study a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belong to the fixed point set of an averaged nonexpansive mapping. We characterize the solu...

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Veröffentlicht in:Applied mathematics & optimization Jg. 87; H. 2; S. 21
Hauptverfasser: Briceño-Arias, Luis, Deride, Julio, López-Rivera, Sergio, Silva, Francisco J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2023
Springer Nature B.V
Springer Verlag (Germany)
Schlagworte:
Algorithms
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Control
Convex analysis
Couplings
Efficiency
Equilibrium
Games
Hilbert space
Inclusions
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Methods
Numerical and Computational Physics
Optimization
Partial differential equations
Simulation
Stochastic programming
Systems Theory
Theoretical
Traffic assignment
65K15
65K05
Constrained LASSO
91-08
Stochastic arc capacity expansion
Monotone operator theory
90C25
Partial inverse method
Constrained convex optimization
90C90
Primal-dual splitting
Mean field games
47H05
ISSN:0095-4616, 1432-0606
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Beschreibung
Zusammenfassung:In this work, we study a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belong to the fixed point set of an averaged nonexpansive mapping. We characterize the solutions using an auxiliary inclusion that involves the partial inverse operator. Then, we propose the primal-dual partial inverse splitting and we prove its weak convergence to a solution of the inclusion, generalizing several methods in the literature. The efficiency of the proposed method is illustrated in multiple applications including constrained LASSO, stochastic arc capacity expansion problems in transport networks, and variational mean field games with non-local couplings.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09921-9