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一部分隐式一部分...
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...
Rosasco, L., Villa, S., Vũ, B.C.: A stochastic inertial forward–backward splitting algorithm for multivariate monotone inclusions. Optimization (2016)L. Rosasco, S. Villa, and B. C. Vu˜, "A stochastic inertial forward-backward splitting algorithm for multivariate monotone inclusions," ...
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 ...
Weak and strong convergences of the generalized penalty Forward–Forward and Forward–Backward splitting algorithms for solving bilevel hierarchical pseudomonotone equilibrium problems Home All Journals Mathematics, Statistics & Data Science Optimization
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 ...
By specialising to two operator inclusions, we recover the forward-reflected-backward and the reflected-forward-backward splitting methods as particular cases. The inspiration for the proposed algorithms arises from interpretations of the aforementioned reflected splitting algorithms as discretisations of the...
In this paper, we study the backward–forward algorithm as a splitting method to solve structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has a natural link with the forward–backward algorithm and has the same computational complexity, since it involves the same...
separately. We show that it is a straightforward extension of a fixed-point algorithm proposed by us as a generalization of the forward–backward splitting algorithm, initially designed for finding a zero of a sum of an arbitrary number of maximally monotone operators∑i=1nAi+B, whereBis cocoer...
While the role of inertia in optimization is well documented, in stochastic splitting problems, the only contribution we are aware of is the work by Rosasco et al. [56]. In that paper asymptotic guarantees for an inertial stochastic forward-backward (SFB) algorithm are presented under the ...