How quasi-Newton can be applied to the objective function of proximal mappings is shown in Section 4. Section 5 introduces the proposed method and algorithms. Section 7 presents the convergence analyses of each
proximal gradient methodVector optimization49J5290C2590C5265K05In this paper, a proximal gradient splitting method for solving nondifferentiable vector optimization problems is proposed. The convergence analysis is carried out when the objective function is the sum of two convex functions where one of...
Becker S, Fadili M (2012) A quasi-newton proximal splitting method. In: Advances in neural information processing systems 25: 26th annual conference on neural information processing systems 2012. Proceedings of a meeting held December 3–6, 2012, Lake Tahoe, Nevada, pp 2627–2635 Blondel M, ...
Deren. A semi-proximal-based strictly contractive Peaceman-Rachford splitting method. Avaliable on http://www.arxiv.org.Gu Y, Jiang B, Han D R. A semi-proximal-based strictly contractive Peaceman-Rachford splitting method. ArXiv: 1506.02221, 2015...
Shen, C., Mi, L., Zhang, L.-H.: An active-set proximal quasi-newton algorithm for \(\ell _1\)-regularized minimization over a sphere constraint. Optimization 71(16), 4623–4664 (2022) Article MathSciNet Google Scholar Shen, C., Wang, Y., Xue, W., Zhang, L.-H.: An acceler...
The numerical approximation of the FSI coupling problem is performed through a splitting strategy, where the fluid and solid sub-problems are solved separately in an iterative way [19], [8]. The nonlinear fluid–structure iterative coupling is performed through a quasi-Newton algorithm adapted from...
We used the interface Quasi-Newton-Implicit Jacobian Least-Squares (IQN-ILS)86 algorithm to couple the discretized governing equations of the fluid and solid domains. The IQN-ILS method has been compared with the monolithic method and other partitioned methods such as Aitken’s dynamic relaxation ...
This paper shows how to perform stable quasi-Newton updating in the multi-batch setting, illustrates the behavior of the algorithm in a distributed computing platform, and studies its convergence properties for both the convex and nonconvex cases. Proximal Stochastic Methods for Nonsmooth, Nonconvex ...
In this paper, a proximal gradient splitting method for solving nondifferentiable vector optimization problems is proposed. The convergence analysis is carried out when the objective function is the sum of two convex functions where one of them is assumed to be continuously differentiable. The ...
splitting proximal point methodlocal equilibriagradient mappingUnlike convex case, a local equilibrium point of a nonconvex Nash-Cournot oligopolistic equilibrium problem may not be a global one. Finding such a point or even a stationary point of this problem is not an easy task. In this paper,...