An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function

Ying Gao and Wenxing Zhang ()
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Ying Gao: University of Electronic Science and Technology of China
Wenxing Zhang: University of Electronic Science and Technology of China

Computational Optimization and Applications, 2023, vol. 85, issue 1, No 9, 263-291

Abstract: Abstract Primal-dual hybrid gradient (PDHG) method is a canonical and popular prototype for solving saddle point problem (SPP). However, the nonlinear coupling term in SPP excludes the application of PDHG on far-reaching real-world problems. In this paper, following the seminal work by Valkonen (Inverse Problems 30, 2014), we devise a variant iterative scheme for solving SPP with nonlinear function by exerting an alternative extrapolation procedure. The novel iterative scheme falls exactly into the proximal point algorithmic framework without any residuals, which indicates that the associated inclusion problem is “nearer” to the KKT mapping induced by SPP. Under the metrically regular assumption on KKT mapping, we simplify the local convergence of the proposed method on contractive perspective. Numerical simulations on a PDE-constrained nonlinear inverse problem demonstrate the compelling performance of the proposed method.

Keywords: Primal-dual hybrid gradient (modified); Proximal point algorithm; Monotone inclusion; Extrapolation; Linearization; Metric regularity; Contraction (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-023-00453-8

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