Related papers: Linear Convergence of Projection Algorithms

It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces,…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…

Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…

The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance…

This paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In…

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…

This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they…

The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…

In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…

This note demonstrates that, for all compact convex sets, high-precision linear minimization can be performed via a single evaluation of the projection and a scalar-vector multiplication. In consequence, if $\varepsilon$-approximate linear…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…

Based on the correspondence of projection to an eigenvalue problem via the underlying group structure, we generalize the projection algorithm proposed by Morrison et al. This algorithm is eligible for large-scale computations, because we…