An Alternating Projection Algorithm for Computing the Nearest Euclidean Distance Matrix

Glunt, W.; Hayden, T. L.; Sung-Hwa, Hong; Wells, J. H.

doi:10.1137/0611042

Cited by 87 publications

(66 citation statements)

References 15 publications

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“…Among all extensions and variants of APM, it is worth mentioning that Dykstra and Boyle [21], [5] found a suitable modification of von Neumann's scheme for closed and convex sets. APM and their variants have been used by many researches to solve problems on a wide variety of applications [4,6,10,22,23,27,29,32,35,36,38].…”

Section: Alternating Projection Methods (Apm)mentioning

confidence: 99%

A symmetry preserving alternating projection method for matrix model updating

Moreno

Datta

Raydan

2009

Mechanical Systems and Signal Processing

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Section: Alternating Projection Methods (Apm)mentioning

confidence: 99%

A symmetry preserving alternating projection method for matrix model updating

Moreno

Datta

Raydan

2009

Mechanical Systems and Signal Processing

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“…Fortunately, fast algorithms are available for (8). For example, the alternating projection method in [31] and the Newton method in [25] both make use of the nice characterization: (−JDJ) 0 if and only if…”

Section: Background On Edm Optimizationmentioning

confidence: 99%

“…A more accurate measurement is between D and D themselves. This leads to the widely studied nearest EDM problem (see, e.g., [31,25] and the references therein):…”

Section: Background On Edm Optimizationmentioning

confidence: 99%

Tackling the flip ambiguity in wireless sensor network localization and beyond

Bai

2016

Digital Signal Processing

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There have been significant advances in range-based numerical methods for sensor network localizations over the past decade. However, there remain a few challenges to be resolved to satisfaction. Those issues include, for example, the flip ambiguity, high level of noises in distance measurements, and irregular topology of the concerning network. Each or a combination of them often severely degrades the otherwise good performance of existing methods. Integrating the connectivity constraints is an effective way to deal with those issues. However, there are too many of such constraints, especially in a large and sparse network. This presents a challenging computational problem to existing methods. In this paper, we propose a convex optimization model based on the Euclidean Distance Matrix (EDM). In our model, the connectivity constraints can be simply represented as lower and upper bounds on the elements of EDM, resulting in a standard 3-block quadratic conic programming, which can be efficiently solved by a recently proposed 3-block alternating direction method of multipliers. Numerical experiments show that the EDM model effectively eliminates the flip ambiguity and retains robustness in terms of being resistance to irregular wireless sensor network topology and high noise levels.

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“…Note that the feasible region is the intersection of two convex sets and the objective is the orthogonal projection of D onto the feasible region. Therefore, 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64alternating projection methods are natural choices (see [13,16]) and they have been used in molecular conformation [17,18]. Problem (25) can also be reformulated as SDP, see [1] and [44].…”

Section: Nearest Edm Problemsmentioning

confidence: 99%

Conditional Quadratic Semidefinite Programming: Examples and Methods

2014

J. Oper. Res. Soc. China

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Abstract:The conditional Quadratic Semidefinite Programming (cQSDP) refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace and the objectives are quadratic. The chief purpose of this paper is to focus on two primal examples of cQSDP: the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem.For the latter problem, we review some classical contributions and establish certain links among them. Moreover, we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy.We also include an application in calibrating the correlation matrix in Libor market models. We hope this work will stimulate new research in cQSDP. Response to Reviewers:The author would like to thank the referees and the associate editor for their efforts in their speedy review. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Conditional Quadratic Semidefinite Programming: Examples and MethodsHou-Duo Qi * April 14, 2014; Revised May 3, 2014 AbstractThe conditional Quadratic Semidefinite Programming (cQSDP) refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace and the objectives are quadratic. The chief purpose of this paper is to focus on two primal examples of cQSDP: the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem. For the latter problem, we review some classical contributions and establish certain links among them. Moreover, we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy. We also include an application in calibrating the correlation matrix in Libor market models. We hope this work will stimulate new research in cQSDP.

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An Alternating Projection Algorithm for Computing the Nearest Euclidean Distance Matrix

Cited by 87 publications

References 15 publications

A symmetry preserving alternating projection method for matrix model updating

A symmetry preserving alternating projection method for matrix model updating

Tackling the flip ambiguity in wireless sensor network localization and beyond

Conditional Quadratic Semidefinite Programming: Examples and Methods

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