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A product space reformulation with reduced dimension for splitting algorithms

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  • Rubén Campoy

    (Universitat de València)

Abstract

In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra’s classical reformulation with a different decomposition, which results in a reduction of the dimension of the outcoming product Hilbert space. We discuss the case of not necessarily convex feasibility and best approximation problems. By applying existing splitting methods to the proposed reformulation we obtain new parallel variants of them with a reduction in the number of variables. The convergence of the new algorithms is straightforwardly derived with no further assumptions. The computational advantage is illustrated through some numerical experiments.

Suggested Citation

  • Rubén Campoy, 2022. "A product space reformulation with reduced dimension for splitting algorithms," Computational Optimization and Applications, Springer, vol. 83(1), pages 319-348, September.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00395-7
    DOI: 10.1007/s10589-022-00395-7
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    References listed on IDEAS

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    1. Minh N. Dao & Neil D. Dizon & Jeffrey A. Hogan & Matthew K. Tam, 2021. "Constraint Reduction Reformulations for Projection Algorithms with Applications to Wavelet Construction," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 201-233, July.
    2. Francisco J. Aragón Artacho & Rubén Campoy, 2018. "A new projection method for finding the closest point in the intersection of convex sets," Computational Optimization and Applications, Springer, vol. 69(1), pages 99-132, January.
    3. Francisco J. Aragón Artacho & Rubén Campoy, 2019. "Computing the Resolvent of the Sum of Maximally Monotone Operators with the Averaged Alternating Modified Reflections Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 709-726, June.
    4. Rieger, Janosch & Tam, Matthew K., 2020. "Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    5. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2016. "Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 148-178, April.
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