Related papers: An Algorithm for Nonsymmetric Conic Optimization I…
Parametric search has been widely used in geometric algorithms. Cole's improvement provides a way of saving a logarithmic factor in the running time over what is achievable using the standard method. Unfortunately, this improvement comes at…
We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is…
We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in $\mathbb{R}^n$ and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such…
This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient…
We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
The stochastic proximal gradient method is a powerful generalization of the widely used stochastic gradient descent (SGD) method and has found numerous applications in Machine Learning. However, it is notoriously known that this method…
Large-scale machine learning models necessitate distributed systems, posing significant design challenges due to the large parameter space across distinct design stacks. Existing studies often focus on optimizing individual system aspects…
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…
Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner…
This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its…