相关论文: Circumcentering the Douglas--Rachford method

Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius…

This paper analyzes the convergence rates of the {\it Frank-Wolfe } method for solving convex constrained multiobjective optimization. We establish improved convergence rates under different assumptions on the objective function, the…

We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…

This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…

The Douglas-Rachford splitting algorithm was originally proposed in 1956 to solve a system of linear equations arising from the discretization of a partial differential equation. In 1979, Lions and Mercier brought forward a very powerful…

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact…

We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…

We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the…

Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned…

This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a…

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…

We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…

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…

We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to…

This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…

In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents…

Newton's method for finding an unconstrained minimizer for strictly convex functions, generally speaking, does not converge from any starting point. We introduce and study the damped regularized Newton's method (DRNM). It converges globally…