Forward–Backward–Half Forward Dynamical Systems for Monotone Inclusion Problems with Application to v-GNE

Pankaj Gautam (), Daya Ram Sahu (), Avinash Dixit () and Tanmoy Som ()
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Pankaj Gautam: Indian Institute of Technology (Banaras Hindu University)
Daya Ram Sahu: Banaras Hindu University
Avinash Dixit: Indian Institute of Technology (Banaras Hindu University)
Tanmoy Som: Indian Institute of Technology (Banaras Hindu University)

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 2, No 6, 523 pages

Abstract: Abstract In this paper, the first-order forward–backward–half forward dynamical systems associated with the inclusion problem consisting of three monotone operators are analyzed. The framework modifies the forward–backward–forward dynamical system by adding a cocoercive operator to the inclusion. The existence, uniqueness, and weak asymptotic convergence of the generated trajectories are discussed. A variable metric forward–backward–half forward dynamical system with the essence of non-self-adjoint linear operators is introduced. The proposed notion, in turn, extends the forward–backward–forward dynamical system and forward–backward dynamical system in the framework of variable metric by relaxing some conditions on the metrics. The distributed dynamical system is further explored to compute a generalized Nash equilibrium in a monotone game as an application. A numerical example is provided to illustrate the convergence of trajectories.

Keywords: Dynamical system; Monotone inclusions; Forward–backward–half forward algorithm; Variable metric; Generalized Nash equilibrium (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01891-2

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