相关论文: Gearhart-Koshy Acceleration for Affine Subspaces
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
Given two disjoint convex polyhedra, we look for a best approximation pair relative to them, i.e., a pair of points, one in each polyhedron, attaining the minimum distance between the sets. Cheney and Goldstein showed that alternating…
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
In the paper we propose an accelerated directional search method with non-euclidian prox-structure. We consider convex unconstraint optimization problem in $\mathbb{R}^n$. For simplicity we start from the zero point. We expect in advance…
Restricting path tracing to a small number of paths per pixel for performance reasons rarely achieves a satisfactory image quality for scenes of interest. However, path space filtering may dramatically improve the visual quality by sharing…
In this paper we propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2) the adaptive gradient method, without any knowledge of the…
In this paper, we present a linear-time approximation scheme for $k$-means clustering of \emph{incomplete} data points in $d$-dimensional Euclidean space. An \emph{incomplete} data point with $\Delta>0$ unspecified entries is represented as…
We propose a linesearch projection algorithm for solving non-monotone and non-Lipschitzian equilibrium problems in Hilbert spaces. It is proved that the sequence generated by the proposed algorithm converges strongly to a solution of the…
The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the…
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection…
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in Quantum Optimal Control Theory (QOCT). We show how the non-linear equations of QOCT can be viewed as a "fixed-point"…
We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS)…
We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps.…
In this paper we show how to accelerate randomized coordinate descent methods and achieve faster convergence rates without paying per-iteration costs in asymptotic running time. In particular, we show how to generalize and efficiently…
The task of finding the optimal compression of a polyline with straight-line segments and arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. Optimal compression algorithms find…