Related papers: Local convergence of alternating low-rank optimiza…
We study the polynomial optimization problem of minimizing a multihomogeneous polynomial over the product of spheres. This polynomial optimization problem models the tensor optimization problem of finding the best rank one approximation of…
Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…
Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…
A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…
In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical problems for which existing relaxations fail…
The epsilon alternating least squares ($\epsilon$-ALS) is developed and analyzed for canonical polyadic decomposition (approximation) of a higher-order tensor where one or more of the factor matrices are assumed to be columnwisely…
In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries can be efficiently approximated by certain functions defined…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets.…
We show that the recent hierarchy of semidefinite programming relaxations based on non-commutative polynomial optimization and reduced density matrix variational methods exhibits an interesting paradox when applied to the bosonic case: even…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…
This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…
To address difficult optimization problems, convex relaxations based on semidefinite programming are now common place in many fields. Although solvable in polynomial time, large semidefinite programs tend to be computationally challenging.…