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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Abstract	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.
AbstractList	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.
ArticleNumber	21
Author	Silva, Francisco J. Deride, Julio López-Rivera, Sergio Briceño-Arias, Luis
Author_xml	– sequence: 1 givenname: Luis surname: Briceño-Arias fullname: Briceño-Arias, Luis organization: Universidad Técnica Federico Santa María – sequence: 2 givenname: Julio orcidid: 0000-0003-4094-8819 surname: Deride fullname: Deride, Julio email: julio.deride@usm.cl organization: Universidad Técnica Federico Santa María – sequence: 3 givenname: Sergio surname: López-Rivera fullname: López-Rivera, Sergio organization: Universidad Técnica Federico Santa María – sequence: 4 givenname: Francisco J. surname: Silva fullname: Silva, Francisco J. organization: Université de Limoges
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Keywords	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
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Snippet	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...
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SubjectTerms	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
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Title	A Primal-Dual Partial Inverse Algorithm for Constrained Monotone Inclusions: Applications to Stochastic Programming and Mean Field Games
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