The Experts below are selected from a list of 6348 Experts worldwide ranked by ideXlab platform
Adam Wierman - One of the best experts on this subject based on the ideXlab platform.
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Newton Polytopes and Relative Entropy Optimization
Foundations of Computational Mathematics, 2021Co-Authors: Riley Murray, Venkat Chandrasekaran, Adam WiermanAbstract:Certifying function Nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications in optimization. We study the question of certifying Nonnegativity of signomials based on the recently proposed approach of Sums-of-AM/GM-Exponentials (SAGE) decomposition due to the second author and Shah. The existence of a SAGE decomposition is a sufficient condition for Nonnegativity of a signomial, and it can be verified by solving a tractable convex relative entropy program. We present new structural properties of SAGE certificates such as a characterization of the extreme rays of the cones associated to these decompositions as well as an appealing form of sparsity preservation. These lead to a number of important consequences such as conditions under which signomial Nonnegativity is equivalent to the existence of a SAGE decomposition; our results represent the broadest-known class of nonconvex signomial optimization problems that can be solved efficiently via convex relaxation. The analysis in this paper proceeds by leveraging the interaction between the convex duality underlying SAGE certificates and the face structure of Newton polytopes. After proving our main signomial results, we direct our machinery toward the topic of globally nonnegative polynomials. This leads to (among other things) efficient methods for certifying polynomial Nonnegativity, with complexity independent of the degree of a polynomial.
Yuya Takeuchi - One of the best experts on this subject based on the ideXlab platform.
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Nonnegativity of the cr paneitz operator for embeddable cr manifolds
Duke Mathematical Journal, 2020Co-Authors: Yuya TakeuchiAbstract:The Nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this Nonnegativity for embeddable CR manifolds. This result gives an affirmative solution to the CR Yamabe problem for embeddable CR manifolds. We also show the existence of a contact form with zero CR Q-curvature and generalize the total Q-prime curvature to embeddable CR manifolds with no pseudo-Einstein contact forms. Furthermore, we discuss the logarithmic singularity of the Szegő kernel.
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Nonnegativity of the cr paneitz operator for embeddable cr manifolds
arXiv: Differential Geometry, 2019Co-Authors: Yuya TakeuchiAbstract:The Nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this Nonnegativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe problem for embeddable CR manifolds. We also show the existence of a contact form with zero CR $Q$-curvature, and generalize the total $Q$-prime curvature to embeddable CR manifolds with no pseudo-Einstein contact forms. Furthermore, we discuss the logarithmic singularity of the Szegő kernel.
Riley Murray - One of the best experts on this subject based on the ideXlab platform.
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Newton Polytopes and Relative Entropy Optimization
Foundations of Computational Mathematics, 2021Co-Authors: Riley Murray, Venkat Chandrasekaran, Adam WiermanAbstract:Certifying function Nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications in optimization. We study the question of certifying Nonnegativity of signomials based on the recently proposed approach of Sums-of-AM/GM-Exponentials (SAGE) decomposition due to the second author and Shah. The existence of a SAGE decomposition is a sufficient condition for Nonnegativity of a signomial, and it can be verified by solving a tractable convex relative entropy program. We present new structural properties of SAGE certificates such as a characterization of the extreme rays of the cones associated to these decompositions as well as an appealing form of sparsity preservation. These lead to a number of important consequences such as conditions under which signomial Nonnegativity is equivalent to the existence of a SAGE decomposition; our results represent the broadest-known class of nonconvex signomial optimization problems that can be solved efficiently via convex relaxation. The analysis in this paper proceeds by leveraging the interaction between the convex duality underlying SAGE certificates and the face structure of Newton polytopes. After proving our main signomial results, we direct our machinery toward the topic of globally nonnegative polynomials. This leads to (among other things) efficient methods for certifying polynomial Nonnegativity, with complexity independent of the degree of a polynomial.
Nicholas D Sidiropoulos - One of the best experts on this subject based on the ideXlab platform.
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nonnegative matrix factorization for signal and data analytics identifiability algorithms and applications
IEEE Signal Processing Magazine, 2019Co-Authors: Kejun Huang, Nicholas D SidiropoulosAbstract:Nonnegative matrix factorization (NMF) aims to factor a data matrix into low-rank latent factor matrices with Nonnegativity constraints.
K C Sivakumar - One of the best experts on this subject based on the ideXlab platform.
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a new characterization of Nonnegativity of moore penrose inverses of gram operators
Positivity, 2009Co-Authors: K C SivakumarAbstract:In this article, a new characterization for the Nonnegativity of Moore–Penrose inverses of Gram operators over Hilbert spaces is presented. The main result generalizes the existing result for invertible Gram operators.
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moore penrose inverse of a gram matrix and its Nonnegativity
Journal of Optimization Theory and Applications, 2008Co-Authors: T Kurmayya, K C SivakumarAbstract:Let M=[A a] be a matrix of order m×n, where A∈ℝm×(n−1) and a∈ℝm is an m×1 vector. In this article, we derive a formula for the Moore-Penrose inverse of M*M and obtain sufficient conditions for its Nonnegativity. The results presented here generalize the ones known earlier.