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Related papers: The Multidimensional Moment Problem with Complexit…

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The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…

Functional Analysis · Mathematics 2008-10-07 Mihai Putinar , Konrad Schmüdgen

Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for an anisotropic problem with a parameter is established. More precisely, a concrete interval of positive parameters, for which the treated…

Analysis of PDEs · Mathematics 2016-08-26 Giovanni Molica Bisci , Dušan Repovš

The aim of this paper is to study the full $K-$moment problem for measures supported on some particular non-linear subsets $K$ of an infinite dimensional vector space. We focus on the case of random measures, that is $K$ is a subset of all…

Functional Analysis · Mathematics 2021-08-16 Maria Infusino , Tobias Kuna

We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…

Optimization and Control · Mathematics 2011-02-25 Florian Bugarin , Didier Henrion , Jean-Bernard Lasserre

The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…

Probability · Mathematics 2024-05-10 Will Sawin , Melanie Matchett Wood

A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…

Functional Analysis · Mathematics 2010-06-08 Ognyan Kounchev , Hermann Render

We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…

Optimization and Control · Mathematics 2025-03-04 Nir Gavish , Guy Katriel

The classic integrated conditional moment test is a promising method for testing regression model misspecification. However, it severely suffers from the curse of dimensionality. To extend it to handle the testing problem for parametric…

Statistics Theory · Mathematics 2020-05-26 Falong Tan , Lixing Zhu

We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P in R^d is a rational function. Its denominator is the product of linear…

Metric Geometry · Mathematics 2018-04-09 Nick Gravin , Dmitrii V. Pasechnik , Boris Shapiro , Michael Shapiro

It is known that positive definiteness is not enough for the multidimensional moment problem to be solved. We would like throw in to the garden of existing in this matter so far results one more, a result which takes into considerations the…

Functional Analysis · Mathematics 2007-06-29 F. H. Szafraniec

The notion of moment differentiation is extended to the set of generalized multisums of formal power series via an appropriate integral representation and accurate estimates of the moment derivatives. The main result is applied to…

Classical Analysis and ODEs · Mathematics 2023-01-03 Alberto Lastra , Sławomir Michalik , Maria Suwińska

We consider the linear conic optimization problem with the cone of nonnegative polynomials. Its dual optimization problem is the generalized moment problem. Moment-SOS relaxations are powerful for solving them. This paper studies finite…

Optimization and Control · Mathematics 2024-07-08 Lei Huang , Jiawang Nie , Ya-Xiang Yuan

Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version asking for sets of variables as…

Computational Complexity · Computer Science 2019-09-18 Yasir Mahmood , Arne Meier , Johannes Schmidt

This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…

Logic in Computer Science · Computer Science 2007-05-23 Stefan Ratschan , Luc Jaulin

In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard…

Logic in Computer Science · Computer Science 2012-12-10 Kshitij Bansal , Stéphane Demri

This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…

Computational Complexity · Computer Science 2013-09-24 Armin Hemmerling

The existence, multiplicity and nonexistence of nontrivial radial convex solutions of a system of two weakly coupled Monge-Ampere equations are established with asymptotic assumptions for an appropriately chosen parameter. The proof of the…

Analysis of PDEs · Mathematics 2010-08-30 Haiyan Wang

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…

Optimization and Control · Mathematics 2017-08-08 Xi Chen , Simai He , Bo Jiang , Christopher Thomas Ryan , Teng Zhang

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

Optimization and Control · Mathematics 2018-01-29 Ning Ruan , David Yang Gao

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…

Computational Complexity · Computer Science 2010-09-13 Michael Thomas , Heribert Vollmer