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

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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.

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Acknowledgements

The work of the first author is supported by Centro de Modelamiento Matemático (CMM) FB210005 BASAL funds for centers of excellence, Redes 180032, and FONDECYT 1190871 from ANID-Chile. The second author is founded by the National Agency for Research and Development (ANID) under grant FONDECYT 11190549, respectively. The third author is founded by the Scholarship program CONICYT-PFCHA/MagísterNacional/2019 - 22190564 and FONDECYT 1190871 of ANID.

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Authors and Affiliations

  1. Universidad Técnica Federico Santa María, Santiago, Chile

    Luis Briceño-Arias, Julio Deride & Sergio López-Rivera

  2. Université de Limoges, Limoges, France

    Francisco J. Silva

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  1. Luis Briceño-Arias
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  2. Julio Deride
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Briceño-Arias, L., Deride, J., López-Rivera, S. et al. A Primal-Dual Partial Inverse Algorithm for Constrained Monotone Inclusions: Applications to Stochastic Programming and Mean Field Games. Appl Math Optim 87, 21 (2023). https://doi.org/10.1007/s00245-022-09921-9

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