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We analyze two communication-efficient algorithms for distributed statistical optimization on large-scale data sets. The first algorithm is a standard averaging method that distributes the $N$ data samples evenly to $\nummac$ machines,…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users' constraint sets, where…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
The quadratic system provided by the Time of Arrival technique can be solved analytically or by optimization algorithms. In practice, a combination of both methods is used. An important problem in quadratic optimization is the possible…
The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able…
Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable…
This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
In the multiuser downlink, power allocation for linear precoders that minimize the sum of mean squared errors under a sum power constraint is a non-convex problem. Many existing algorithms solve an equivalent convex problem in the virtual…
In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
We consider the consensual distributed optimization problem in the Riemannian context. Specifically, the minimization of a sum of functions form is studied where each individual function in the sum is located at the node of a network. An…
In this paper, we investigate the distributed convex optimization problem over a multi-agent system with Markovian switching communication networks. The objective function is the sum of each agent's local objective function, which cannot be…
We consider Bayesian inference of signals with vector-valued entries. Extending concentration techniques from the mathematical physics of spin glasses, we show that the matrix-valued minimum mean-square error concentrates when the size of…
We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…
In this work we study the problem of unconstrained convex-optimization in a fully distributed multi-agent setting which includes asynchronous computation and lossy communication. In particular, we extend a recently proposed algorithm named…