A. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl., 12(1-3):13--30, 1999. Computational optimization---a tribute to Olvi Mangasarian, Part I. Home/Search Document Details and Download
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Polynomial Instances Of The Positive Semidefinite And Euclidean.. - Laurent (1998) (2 citations) (Correct)
....1.3. Back to the matrix completion problem. As the matrix completion problem is a special instance of SDP, it can be solved approximatively in polynomial time; specific interior point algorithms for finding approximate psd and distance matrix completions have been developed, e.g. in [19] 10] [2], 30] However, such algorithms are not garanteed to find exact completions in polynomial time. This motivates our study in this paper of some classes of matrix completion problems that can be solved exactly in polynomial time. As mentioned earlier, one of the difficulties in the complexity ....
A.Y. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semidefinite programming. Computational Optimization and Applications, 12:13-- 30, 1998.
Matrix Completion Problems - Laurent (2001) (2 citations) (Correct)
....In view of relation (6) problem (EDM) can be formulated as an instance of the semidefinite programming problem (P) and, therefore, it can be solved with an arbitrary precision in polynomial time. Exploiting this fact, some specific algorithms based on interior point methods are presented in [AKW97] together with numerical tests. Moreover, problem (EDM) can be solved in polynomial time when restricted to partial rational matrices whose pattern is a chordal graph or, more generally, a graph with fixed minimum fill in [La98d] as in the psd case, this follows from the fact (mentioned below) ....
A.Y. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semidefinite programming. Technical Report CORR 97-9, University of Waterloo, 1997. To appear in Computational Optimization and Applications.
Comparison of Public-Domain Software for Black-Box .. - Mongeau.. (1998) (6 citations) (Correct)
.... consists in solving the following global optimization problem: min ;b f( b) where f( b) median r 2 i ( b) r i ( b) y i Gamma x i1 1 Gamma : Gamma x ip p Gamma b; 4 Problem dimension source application box constraints lms1a 1 [16, chap.2, table 2] [0,1] lms1b 1 [16, chap.2, table 3] least median [ 2,6] lms2 2 [16, chap.3, table 23] of squares [0,3] lms3 3 [16, chap.3, table 1] regression [ 2,2] lms5 5 [16, chap.3, table 2] 2.5,2.5] pf3 9 pf4 12 [17] protein [ 1,1] pf5 15 folding pf6 18 ms1 20 [10] multidimensional [ 2.67,2.67] ms2 20 scaling ....
....Problem dimension source application box constraints lms1a 1 [16, chap.2, table 2] 0,1] lms1b 1 [16, chap.2, table 3] least median [ 2,6] lms2 2 [16, chap.3, table 23] of squares [0,3] lms3 3 [16, chap.3, table 1] regression [ 2,2] lms5 5 [16, chap.3, table 2] 2.5,2. 5] pf3 9 pf4 12 [17] protein [ 1,1] pf5 15 folding pf6 18 ms1 20 [10] multidimensional [ 2.67,2.67] ms2 20 scaling [ 3.27,3.27] Table 1: Test Problems and the points (y i ; x i1 ; x ip ) are given. In other words, this problem is that of finding a hyperplane in IR p 1 from which (at least) half of the given points lie ....
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A. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semidefinite programming. Computational Optimization and Applications, 12:13--30, 1998.
Multidimensional Scaling - de Leeuw (2001) (1 citation) (Correct)
....configuration is constructed from a subset of the distances, and at the same time the other (missing) distances are estimated. Such distance completion problems (in which we assume that the observed distances are measured without error) are currently solved with mathematical programming methods (Alfakih, Khandani Wolkowicz 1998). 2.3. Three way Scaling. In three way scaling we have information on dissimilarities between n objects on m occasions, or for m subjects. Two easy ways of dealing with the occasions is to perform either a separate MDS for each subject or to perform a single MDS for the average occasion. In ....
Alfakih, A., Khandani, A. & Wolkowicz, H. (1998), `Solving Euclidean distance matrix completion problems via semidefinite programming', Computational Optimization and Applications 12, 13--30.
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A. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl., 12(1-3):13--30, 1999. Computational optimization---a tribute to Olvi Mangasarian, Part I.
Euclidean Distance Matrices - And The Molecular Self-citation (Alfakih Wolkowicz) (Correct)
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A. Y. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semide nite programming. Comput. Optim. Appl., 12:13-30, 1999.
Approximate and Exact Completion Problems for Euclidean.. - Suliman Al-Homidan Henry Self-citation (Wolkowicz) (Correct)
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A. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl., 12(1-3):13--30, 1999. Computational optimization---a tribute to Olvi Mangasarian, Part I.
Semidefinite and Cone Programming Bibliography/Comments - Wolkowicz (2004) Self-citation (Wolkowicz) (Correct)
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A. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl., 12(1-3):13--30, 1999. Computational optimization---a tribute to Olvi Mangasarian, Part I.
Semidefinite and Cone Programming Bibliography/Comments - Wolkowicz (2001) Self-citation (Wolkowicz) (Correct)
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A. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidenite programming. Comput. Optim. Appl., 12(1-3):13-30, 1999. Computational optimization|a tribute to Olvi Mangasarian, Part I.
Semidefinite Programming for Discrete Optimization and.. - Wolkowicz, Anjos (2000) Self-citation (Wolkowicz) (Correct)
....theoretical existence results for completions based on chordality. This follows the work in [41] An approach to solving large sparse completion problems based on approximate completions [56] is outlined in Section 5.2. In Section 5. 3 a similar approach for Euclidean distance matrix completions [1] is presented. However, the latter does not take advantage of sparsity and has diculty solving large sparse problems. We conclude in Section 5.4 with a new characterization of Euclidean distance matrices from which we derive an algorithm that successfully exploits sparsity [118] 1.1 Notation and ....
....for completions based on chordality. This follows the work in [41] We then present an ecient approach to solve PSDM completion problems [56] This approach successfully solves large sparse problems. In Section 5. 3 this approach is extended to the EDM completion problem (based on the work in [1]) but is shown to exhibit diculties in the large sparse case. Hence we conclude by presenting in Section 5.4 a new characterization of Euclidean distance matrices and new algorithms that eciently solve large sparse problems. 5.1 Existence Results Both the PSDM and EDM problems have been ....
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A. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidenite programming. Comput. Optim. Appl., 12(1-3):13-30, 1999. Computational optimization|a tribute to Olvi Mangasarian, Part I.
On the Embeddability of Weighted Graphs in Euclidean Spaces - Alfakih, Wolkowicz (1998) (3 citations) Self-citation (Alfakih Wolkowicz) (Correct)
....First, the EDMCP is a convex problem which can be solved in polynomial time with an arbitrary precision. Second, the EDMCP r is intractable since restricting the rank of X to r destroys the convexity of the problem. EDMCP is solved using a Primal Dual Interior Point algorithm introduced in [2]. Due to the nature of Interior Point methods, optimal solutions of large ranks are often obtained. Rounding this optimal solution into another one with a lower rank necessitates the study of the set of optimal solution of EDMCP in the next section 3 Set of Optimal Solutions of EDMCP Let X be ....
A. Y. ALFAKIH, A. KHANDANI, and H. WOLKOWICZ. Solving Euclidean distance matrix completion problems via semidefinite programming. Technical report, CORR 97-9, Dept. of combinatorics and optimization, University of Waterloo, 1997.
On Least Squares Euclidean Distance Matrix - Approximation And Completion (Correct)
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A. Alfakih, A. Khandani, and H. Wolkowicz, Solving Euclidean distance matrix completion problems via semidefinite programming, Comput. Optim. Appl., 12(1999), pp.13-30.
Comparison of Public-Domain Software for Black Box .. - Mongeau.. (1998) (6 citations) (Correct)
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A. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semide nite programming. Computational Optimization and Applications, 12:13-30, 1998.
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Abdo Y. Alfakih, Amir Khandani, and Henry Wolkowicz, "Solving Euclidean distance matrix completion problems via semidefinite programming, " Comput. Optim. Appl., vol. 12, no. 1-3, pp. 13--30, 1999.
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A. Y. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl., 12(1-3):13--30, November 1999.
Rigidity, Computation, and Randomization in Network.. - Eren, Goldenberg.. (2004) (1 citation) (Correct)
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Abdo Y. Alfakih, Amir Khandani, and Henry Wolkowicz, "Solving Euclidean distance matrix completion problems via semidefinite programming, " Comput. Optim. Appl., vol. 12, no. 1-3, pp. 13--30, 1999.
SIAG/OPT Views-and-News - Forum For The (Correct)
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A. Y. Alfakih, A. Khandani, and H. Wolkowicz, Solving Euclidean distance matrix completion problems via semidefinite programming, Comput. Optim. Appl., 12 (1999), pp. 13--30.
Extensions of Classical Multidimensional Scaling: Computational.. - Trosset (Correct)
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Alfakih, A. Y., Khandani, A., and Wolkowicz, H. (1998). Solving Euclidean distance matrix completion problems via semide nite programming. Computational Optimization and Applications, 12:13-30.
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