Related papers: CS-TSSOS: Correlative and term sparsity for large-…
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…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
Lasserre's moment-SOS hierarchy consists of approximating instances of the generalized moment problem (GMP) with moment relaxations and sums-of-squares (SOS) strenghtenings that boil down to convex semidefinite programming (SDP) problems.…
Semidefinite and sum-of-squares (SOS) optimization are fundamental computational tools in many areas, including linear and nonlinear systems theory. However, the scale of problems that can be addressed reliably and efficiently is still…
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
This paper studies the matrix Moment-SOS hierarchy for solving polynomial matrix optimization. Our first result is to show the finite convergence of this hierarchy, if the nondegeneracy condition, strict complementarity condition and second…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Tensor Compressive Sensing (TCS) is a multidimensional framework of Compressive Sensing (CS), and it is advantageous in terms of reducing the amount of storage, easing hardware implementations and preserving multidimensional structures of…
The classical Moment-Sum Of Squares hierarchy allows to approximate a global minimum of a polynomial optimization problem through semidefinite relaxations of increasing size. However, for many optimization instances, solving higher order…
Global optimization has gained attraction over the past decades, thanks to the development of both theoretical foundations and efficient numerical routines. Among recent advances, Kernel Sum of Squares (KernelSOS) provides a powerful…
We propose general notions to deal with large scale polynomial optimization problems and demonstrate their efficiency on a key industrial problem of the twenty first century, namely the optimal power flow problem. These notions enable us to…
CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…
We identify a new sufficient condition for the finite convergence of moment relaxations of polynomial optimization problems with correlative sparsity. This condition, which follows from a solution to a correlatively sparse version of the…
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…