相关论文: Stochastic Halpern Iteration with Variance Reducti…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each iteration of these algorithms require one forward evaluation…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
This paper is based on Tseng's exgradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the assumptions that the cost operator is quasimonotone and Lipschitz continuous, we establish the strong…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…
We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…
We investigate the asymptotic behavior of Halpern-type iterations applied to quasi-nonexpansive operators arising in best approximation problems over the intersection of finitely many closed convex sets in $\mathbb{R}^n$. Assuming a local…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
Monotone inclusions involving the sum of three maximally monotone operators or more have received much attention in recent years. In this paper, we propose three splitting algorithms for finding a zero of the sum of four monotone operators,…
This paper proposes a framework to study the convergence of stochastic optimization and learning algorithms. The framework is modeled over the different challenges that these algorithms pose, such as (i) the presence of random additive…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
In our pursuit of finding a zero for a monotone and Lipschitz continuous operator $M : \R^n \rightarrow \R^n$ amidst noisy evaluations, we explore an associated differential equation within a stochastic framework, incorporating a correction…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…
Osborne's iteration is a method for balancing $n\times n$ matrices which is widely used in linear algebra packages, as balancing preserves eigenvalues and stabilizes their numeral computation. The iteration can be implemented in any norm…
In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng's…
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…