Related papers: Generalized truncated moment problems with unbound…
In this paper we develop a new approximation method valid for a wide family of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a reduced set of ordinary differential equations for a finite set of parameters measuring…
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…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
Let $K_f$ be a closed semi-algebraic set in $\dR^d$ such that there exist bounded real polynomials $h_1,{...},h_n$ on $K_f$. It is proved that the moment problem for $K_f$ is solvable provided it is for all sets $K_f\cap C_\lambda$, where…
We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
In this paper, we present a branch and bound algorithm for extracting approximate solutions to Global Polynomial Optimization (GPO) problems with bounded feasible sets. The algorithm is based on a combination of SOS/Moment relaxations and…
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher…
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…
This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper we obtain a Nevanlinna-type formula for this moment problem…
Moment matching is an easy-to-implement and usually effective method to reduce variance of Monte Carlo simulation estimates. On the other hand, there is no guarantee that moment matching will always reduce simulation variance for general…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
An atomic random complex measure defined on the unit disk with Normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving…
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…
The moment-sum-of-squares (moment-SOS) hierarchy is one of the most celebrated and widely applied methods for approximating the minimum of an n-variate polynomial over a feasible region defined by polynomial (in)equalities. A key feature of…
We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of…
The classical Truncated Moment problem asks for necessary and sufficient conditions so that a linear functional $L$ on $\mathcal{P}_{d}$, the vector space of real $n$-variable polynomials of degree at most $d$, can be written as integration…
We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
We formulate a class of nonlinear {evolution} partial differential equations (PDEs) as linear optimization problems on moments of positive measures supported on infinite-dimensional vector spaces. Using sums of squares (SOS) representations…