这类算法里面最简单的就是投影梯度法，投影是backward，梯度是forward。稍微扩展一下就是Proximal Gradient...
从ODE角度看 优化算法是在离散梯度流$\dot X=-\nabla f(x)$ 然后做operator splitting 一部分隐式...
Forward-Backward Splitting Algorithm: Goldstein T, Studer C, Baraniuk R. A field guide to forward-backward splitting with a FASTA implementation[J]. arXiv preprint arXiv:1411.3406, 2014. 这篇文章非常棒,对FBSA算法有个非常直观的解释:
Forward-backward splittingLegendre functionMonotone operatorWe establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far been ...
Bredies, K.: A forward-backward splitting algorithm for the minimization of non-smooth con- vex functionals in Banach space. Inverse Problems 25(1), 015,005 (2009)K. Bredies. A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space. Inverse...
Generalized forward–backward splitting with penalization for monotone inclusion problemsMathematics - Optimization and ControlWe introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators...
Pesquet, "Stochastic approximations and perturbations in forward-backward splitting for monotone operators," Pure Appl. Funct. Anal., vol. 1, no. 1, pp. 13-37, Jan. 2016.P. L. Combettes and J.-C. Pesquet, "Stochastic approximations and per- turbations in forward-backward splitting for ...
We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces...
一种迭代优化算法，例如prox-linear算法：从一个初始点出发，向前是沿着数据项函数梯度往前走一步，后向...
Forward–backward methodTseng’s methodOperator splitting methodIn this paper we propose an explicit algorithm for solving a variational inclusion problem of the sum of two operators, the one is maximally monotone and the other is monotone and Lipschitz continuous. The algorithm uses the variable ...