Related papers: Projection onto cones generated by epigraphs of pe…

In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…

The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone…

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…

An approximate projection onto the tangent cone to the variety of third-order tensors of bounded tensor-train rank is proposed and proven to satisfy a better angle condition than the one proposed by Kutschan (2019). Such an approximate…

This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…

A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…

In this paper, we study the generalized differentiability of the metric projection operator onto the positive cone in Hilbert spaces. We first establish the formula for exactly computing the regular coderivative and the Mordukhovich…

Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…

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…

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…

This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To…

This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…

Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates ${u_n}$ converges weakly to a point in the…

We propose new algebraic methods for extracting cylinders and cones from minimal point sets, including oriented points. More precisely, we are interested in computing efficiently cylinders through a set of three points, one of them being…

Recently wide application in engineering-economic problems was received with problems of vector optimization. Development of methods of the decision of these problems it is executed in works A. Messac and others. Complexity of the offered…

We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established involving Newton product projectors on spaces of holomorphic functions on a neighborhood of a…

We investigate projection constants within classes of multivariate polynomials over finite-dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous…