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This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…

Numerical Analysis · Mathematics 2009-11-30 Thomas Blumensath

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Optimization and Control · Mathematics 2016-08-18 Qia Li , Yuesheng Xu , Na Zhang

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…

Numerical Analysis · Mathematics 2016-12-14 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen , Hui Liu

Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…

Probability · Mathematics 2025-03-11 Soumik Pal , Bodhisattva Sen , Ting-Kam Leonard Wong

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…

Machine Learning · Computer Science 2019-09-10 Ibrahim Jubran , Dan Feldman

Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…

Mathematical Physics · Physics 2023-12-15 P. Zhevandrov , A. Merzon , M. I. Romero Rodríguez , J. E. De la Paz Méndez

Given a subset K of the unit Euclidean sphere, we estimate the minimal number m = m(K) of hyperplanes that generate a uniform tessellation of K, in the sense that the fraction of the hyperplanes separating any pair x, y in K is nearly…

Probability · Mathematics 2013-09-27 Yaniv Plan , Roman Vershynin

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

Machine Learning · Computer Science 2020-06-17 Grigory Malinovsky , Dmitry Kovalev , Elnur Gasanov , Laurent Condat , Peter Richtárik

We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Austine Efut Ofem , Kalu Okam Okorie , Chinedu Izuchukwu , Chibueze Christian Okeke

For a finite set $A\subset \mathbb{R}^d$, let $\Delta(A)$ denote the spread of $A$, which is the ratio of the maximum pairwise distance to the minimum pairwise distance. For a positive integer $n$, let $\gamma_d(n)$ denote the largest…

Combinatorics · Mathematics 2022-12-20 Adrian Dumitrescu , Csaba D. Tóth

This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…

Machine Learning · Statistics 2021-02-16 Minh Ha Quang

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…

Optimization and Control · Mathematics 2009-11-04 Augusto Ferrante , Federico Ramponi , Francesco Ticozzi

A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…

Functional Analysis · Mathematics 2009-05-22 P. L. Combettes , N. N. Reyes

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…

Optimization and Control · Mathematics 2024-06-11 Douglas S. Gonçalves , Max L. N. Gonçalves , Jefferson G. Melo

A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of…

Optimization and Control · Mathematics 2017-01-24 Patrick R. Johnstone , Pierre Moulin

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…

Artificial Intelligence · Computer Science 2025-12-09 Rasul Tutunov , Alexandre Maraval , Antoine Grosnit , Xihan Li , Jun Wang , Haitham Bou-Ammar

The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…

Optimization and Control · Mathematics 2026-03-02 Sanjay Manoj , Melkior Ornik

Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…

Numerical Analysis · Mathematics 2022-06-28 Said Kerrache , Yasushi Nakauchi

In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a…

Systems and Control · Electrical Eng. & Systems 2025-03-05 Zihao Ren , Lei Wang , Zhengguang Wu , Guodong Shi

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…

Optimization and Control · Mathematics 2017-11-21 Radu Ioan Bot , Ernö Robert Csetnek , Dennis Meier