Random Activations in Primal-Dual Splittings for Monotone Inclusions with a Priori Information

Luis Briceño-Arias (), Julio Deride () and Cristian Vega ()
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Luis Briceño-Arias: Universidad Técnica Federico Santa María
Julio Deride: Universidad Técnica Federico Santa María
Cristian Vega: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 1, No 3, 56-81

Abstract: Abstract In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a priori information set is represented by the intersection of fixed point sets of a finite number of operators, and we propose an algorithm that activates the corresponding set by following a finite-valued random variable at each iteration. Our formulation is flexible and includes, for instance, deterministic and Bernoulli activations over cyclic schemes, and Kaczmarz-type random activations. The almost sure convergence of the algorithm is obtained by means of properties of stochastic Quasi-Fejér sequences. We also recover several primal-dual algorithms for monotone inclusions without a priori information and classical algorithms for solving convex feasibility problems and linear systems. In the context of convex optimization with inequality constraints, any selection of the constraints defines the a priori information set, in which case the operators involved are simply projections onto half spaces. By incorporating random projections onto a selection of the constraints to classical primal-dual schemes, we obtain faster algorithms as we illustrate by means of a numerical application to a stochastic arc capacity expansion problem in a transport network.

Keywords: Arc capacity expansion in traffic networks; Monotone operator theory; Primal-dual splitting algorithms; Randomized Kaczmarz algorithm; Stochastic Quasi-Fejér sequences; 47H05; 49M29; 90B15; 65K10; 65K05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-021-01944-6

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