Related papers: A Quadratically Convergent Alternating Projection …
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
The convex feasibility problem asks to find a point in the intersection of a collection of nonempty closed convex sets. This problem is of basic importance in mathematics and the physical sciences, and projection (or splitting) methods…
This paper deals with the convex feasibility problem, where the feasible set is given as the intersection of a (possibly infinite) number of closed convex sets. We assume that each set is specified algebraically as a convex inequality,…
We investigate convergence of alternating Bregman projections between non-convex sets and prove convergence to a point in the intersection, or to points realizing a gap between the two sets. The speed of convergence is generally sub-linear,…
We observe that the characteristic polynomial of a linearly perturbed semidefinite matrix can be used to give the convergence rate of alternating projections for the positive semidefinite cone and a line. As a consequence, we show that such…
In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm,…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…
In this paper, we first propose a new Levenberg-Marquardt method for solving constrained (and not necessarily square) nonlinear systems. Basically, the method combines the unconstrained Levenberg-Marquardt method with a type of feasible…
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence…
The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on the feasible set is computed, allowing for an appropriate…
The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets $A,B$ under a mild regularity hypothesis on one of the sets. We…
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…
We provide new conditions under which the alternating projection sequence converges in norm for the convex feasibility problem where a linear subspace with finite codimension $N\geq 2$ and a lattice cone in a Hilbert space are considered.…
This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…
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…
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active…