Related papers: Approximating distribution functions by iterated f…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
We consider the distributed optimization problem for the sum of convex functions where the underlying communications network connecting agents at each time is drawn at random from a collection of directed graphs. Building on an earlier work…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of…
In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous…
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…
We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…