Related papers: A Relax-and-Round Approach to Complex Lattice Basi…
We study the Regularized A-optimal Design (RAOD) problem, which selects a subset of $k$ experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian…
Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization…
We develop and analyze a new `relax-and-split' (RS) approach for compositions of separable nonconvex nonsmooth functions with linear maps. RS uses a relaxation technique together with partial minimization, and brings classic techniques…
Relaxed models are abstract problem descriptions generated by ignoring constraints that are present in base-level problems. They play an important role in planning and search algorithms, as it has been shown that the length of an optimal…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…
In this paper, we propose a simple global optimisation algorithm inspired by Pareto's principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the…
Ab initio atomic relaxations often take large numbers of steps and long times to converge. An atomic relaxation method based on on-the-flight force learning and a corresponding new curved line minimization algorithm is presented to…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…
We study the similarity search problem which aims to find the similar query results according to a set of given data and a query string. To balance the result number and result quality, we combine query result diversity with query…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
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…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…