Related papers: Best approximation in max-plus semimodules
We consider an enhanced version of the well-kwown "Petrov-Galerkin" projection in Hilbert spaces. The proposed procedure, dubbed "multi-slice" projector, exploits the fact that the sought solution belongs to the intersection of several…
Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…
The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…
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…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the…
Problems of quadratic optimization in Hilbert space often arise when solving ill-posed problems for differential equations. In this case, the target value of the functional is known. In addition, the structure of the functional allows…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…
We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
This paper summarizes results on some topics in the max-plus convex geometry, mainly concerning the role of multiorder, Kleene stars and cyclic projectors, and relates them to some topics in max algebra. The multiorder principle leads to…
Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…
In this paper, we proposed an alternating projection based algorithm to solve a class of distributed MIN-MAX convex optimization problems. We firstly transform this MINMAX problem into the problem of searching for the minimum distance…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
In this paper we present a new iterative projection method for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method, termed AAMR for averaged alternating modified reflections,…
We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition. Given a set of samples, each consisting of the input and…