Convex Optimization & Euclidean Distance Geometry

By J. Dattorro. 2004

723 citations recorded by the source corpus.

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Citations in the corpus

Sinkhorn Distances: Lightspeed Computation of Optimal Transport (2013, methodology): “tions obtained when computing d M;(x;y) and d M;(y;z) respectively. Using the matrix Sof U (x;z) provided in Lemma 1, we proceed with the following 19n;9’ 1; ;’ d 2Rn such that m ij = k’ i ’ jk2 2 (Dattorro, 2005, §5). Recall that, in that case, M:t = [mt ij ], 0 < t < 1 is also a Euclidean di”
Computational Optimal Transport (2018, methodology): “Hilbertian distances have many favorable properties when used in a data analysis context [Dattorro, 2017].”
Path Integral Policy Improvement with Covariance Matrix Adaptation (2012, background): “Temporal averaging over covariance matrices is possible, because 1) every positive-semideﬁnite matrix is a covariance matrix and vice versa 2) a weighted averaging over positive-semideﬁnite matrices yields a positive-semideﬁnite matrix (Dattorro, 2011).”
Private Weighted Random Walk Stochastic Gradient Descent (2020, methodology): “( a ) follows from W being a convex closed set, so one can apply nonexpansivity theorem [39, Fact E.9.0.0.5], ( b ) follows from Jensen’s inequality applied to the squared norm.”
Efficient Output Kernel Learning for Multiple Tasks (2015, result): “Proof: It has been shown in [2] and [23][p.”
MIMO Configurations for Relay Channels: Theory and Practice (2007, background): “N ×N Hermitian matrix S and diagonal matrix Σ, we have the following identity [33]:”
Optimizing linear counting queries under differential privacy (2009, background): “Dattorro [4] shows that solving a semidefinite program with rank constraints can be converted into solving two semidefinite programs iteratively.”
Generating valid Euclidean distance matrices (2019, background): “However trying to use this relationship directly in the context of deep learning by parameterizing the matrix D̃ poses a problem, as the set of EDMs forms a cone ([35]) and not a vector space, which is the underlying assumption of the standard optimizers in common deep learning frameworks.”
Euclidean Distance Matrices: Essential theory, algorithms, and applications (2015, background): “An extensive treatise on EDMs with many original results and an elegant characterization of the EDM cone is given by Dattorro [20].”
Online linear optimization with the log-determinant regularizer (2017, background): “For a differentiable function R : Rm×n → R, its gradient ∇R(X) is the m×n matrix whose (i, j)-th componet is ∂R(X) ∂Xi,j , and its Hessian ∇ (2)R(X) is the mn×mn matrix whose ((i, j), (k, l))-th component is ∂ (2)R(X) ∂Xi,j∂Xk,l [20].”
A new embedding quality assessment method for manifold learning (2011, background): “For convenience of presentation, we first introduce the δ operator [39], which is defined as follows”
Distance geometry and data science (2019, methodology): “Proof First, we remark that, given a realization x ∶ V → ℝn , its Gram matrix is X = xx⊤ , and its squared Euclidean distance matrix (EDM) is: Next, we recall that: by Dattorro (2015) after Schoenberg 1935—see (Liberti and Lavor 2016, §7) for a direct proof3.”
MIPLIB 2010 - Mixed Integer Programming Library version 5 (2011, unknown): “Dattorro [43,110] Model to find solution to the “Eternity II” puzzle [112] dfn-gwin-UUM, germany50-DBM, janos-usDDM, nobel-eu-DBE, zib54-UUE C.”
Euclidean Distance Geometry and Applications (2012, background): “As is well known, DG has strong connections to matrix analysis, semidefinite programming (SDP), convex geometry, and graph rigidity [56].”
ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions (2013, methodology): “By exploiting a convex program using the Fantope projection (Overton and Womersley 1992; Dattorro 2005), Vu et al. (2013) showed that there exist computationally efficient estimators that attain (under various settings) OP(s √ log d/n) rate of convergence for possibly nonspike model.”
Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors (2008, methodology): “On a logarithmic scale, (7) uses the Lp distance for the quantitative factors and the 0-1 distance for the qualitative factors.”