Related papers: A Relax-and-Round Approach to Complex Lattice Basi…

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…

In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…

This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient and necessary condition for the sparse hierarchy to be tight.…

This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…

Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial $7$-approximation that is based on a matroid intersection approach, two tight LP-based $3$-approximations were…

Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to…

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…

In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of…

Many learning tasks, such as cross-validation, parameter search, or leave-one-out analysis, involve multiple instances of similar problems, each instance sharing a large part of learning data with the others. We introduce a robust framework…

Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…

A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown…