Related papers: The Chen-Teboulle algorithm is the proximal point …

For solving constrained (pseudo)-monotone variational inequality, we prove that the upper bound of stepsize $\frac{1}{2L}$ established for the Popov's algorithm and the forward-reflected-backward algorithm is tight. For unconstrained case,…

In this paper the degenerate preconditioned proximal point algorithm will be combined with the idea of varying preconditioners leading to the degenerate variable metric proximal point algorithm. The weak convergence of the resulting…

This paper develops a parameter-free adaptive proximal bundle method with two important features: 1) adaptive choice of variable prox stepsizes that "closely fits" the instance under consideration; and 2) adaptive criterion for making the…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function $f(x)$ defined on an interval $[a,b]$ is "rounded" to a prescribed precision by constructing a…

We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…

We obtain existence and convergence theorems on two variants of the proximal point algorithm for proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.

In this work, we establish convergence results for the distributed proximal point algorithm (DPPA) for distributed optimization problems. We consider the problem on the whole domain Rd and find a general condition on the stepsize and cost…

New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…

We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a "large approximately rank-one submatrix". This LAROS problem is used to sequentially extract features in data. We also develop a new stopping…

(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of…

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

In some situations, EM algorithm shows slow convergence problems. One possible reason is that standard procedures update the parameters simultaneously. In this paper we focus on finite mixture estimation. In this framework, we propose a…

We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…

Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme…