Related papers: Optimization over Structured Subsets of Positive S…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its…
Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…
This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an…
The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…