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The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal…

In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century when Carl Friedrich Gauss developed the…

Alternating projection method has been used in a wide range of engineering applications since it is a gradient-free method (without requiring tuning the step size) and usually has fast speed of convergence. In this paper, we formalize two…

The idea of a finite collection of closed sets having "strongly regular intersection" at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically,…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…

In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…

We propose a study of the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding…

This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…

This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…

With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…

This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…

This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…

The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that the discrete uniformizations approximate the continuous…

We analyze the convergence rate of the randomized Newton-like method introduced by Qu et. al. (2016) for smooth and convex objectives, which uses random coordinate blocks of a Hessian-over-approximation matrix $\bM$ instead of the true…

In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…