Related papers: Minimization Problems Based on Relative $\alpha$-E…

Let $L_1,L_2,\dots,L_K$ be a family of closed subspaces of a Hilbert space $H$, $L_1\cap \dots \cap L_K =\{0\}$; let $P_k$ be the orthogonal projection onto $L_k$. We consider two types of consecutive projections of an element $x_0\in H$:…

We study minimizing cones in the Alt-Phillips problem when the exponent {\gamma} is close to 1. When {\gamma} converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise,…

In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…

This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

In this paper we empirically evaluate biased methods for alpha-divergence minimization. In particular, we focus on how the bias affects the final solutions found, and how this depends on the dimensionality of the problem. We find that (i)…

This work is concerned with the minimization of quantum entropies under local constraints of density, current, and energy. The problem arises in the work of Degond and Ringhofer about the derivation of quantum hydrodynamical models from…

We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…

Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…

This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the stiff matrix, of the subspace projection…

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

We systematically explore a class of constrained optimization problems with linear objective function and constraints that are linear combinations of logarithms of the optimization variables. Such problems can be viewed as a generalization…

Random projection techniques based on Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preserving their optimal values, that leads to smaller-scale…

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…

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…

A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…

We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…