Related papers: Linear Convergence of Projection Algorithms
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been…
This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the…
In this paper, we introduce and study the Parallel Polyhedral Projection Method (3PM) and the Approximate Parallel Polyhedral Projection Method (A3PM) for finding a point in the intersection of finitely many closed convex sets. Each…
The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…
The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…
Recommender systems can be characterized as software solutions that provide users convenient access to relevant content. Traditionally, recommender systems research predominantly focuses on developing machine learning algorithms that aim to…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…