-
1
-
-
0002740666
-
Solving Euclidean distance matrix completion problems via semidefinite programming
-
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.
-
(1999)
Comput. Optim. Appl.
, vol.12
, pp. 13-30
-
-
Alfakih, A.Y.1
Khandani, A.2
Wolkowicz, H.3
-
2
-
-
23044487729
-
Approximate and exact completion problems for Euclidean distance matrices using semidefinite programming
-
S. Al-Homidan and H. Wolkowicz, Approximate and exact completion problems for Euclidean distance matrices using semidefinite programming, Linear Algebra Appl., 406 (2005), pp. 109-141.
-
(2005)
Linear Algebra Appl.
, vol.406
, pp. 109-141
-
-
Al-Homidan, S.1
Wolkowicz, H.2
-
3
-
-
0031141136
-
Complementarity and nondegeneracy in semidefinite programming
-
F. Alizadeh, J.-P. A. Haeberly, M. L. Overton, Complementarity and nondegeneracy in semidefinite programming, Math. Program., 77 (1997), pp. 111-128.
-
(1997)
Math. Program.
, vol.77
, pp. 111-128
-
-
Alizadeh, F.1
Haeberly, J.-P.A.2
Overton, M.L.3
-
4
-
-
85014561619
-
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
-
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sciences, 2 (2009), pp. 183-202.
-
(2009)
SIAM J. Imaging Sciences
, vol.2
, pp. 183-202
-
-
Beck, A.1
Teboulle, M.2
-
5
-
-
0003713964
-
-
2nd ed., Athena Scientific, Nashua, NH
-
D. P. Bertsekas, Nonlinear Programming, 2nd ed., Athena Scientific, Nashua, NH, 1999.
-
(1999)
Nonlinear Programming
-
-
Bertsekas, D.P.1
-
6
-
-
0003562364
-
-
2nd ed., Springer Ser. Statist., Springer, New York
-
I. Borg and P. J. F. Groenen, Modern Multidimensional Scaling: Theory and Applications, 2nd ed., Springer Ser. Statist., Springer, New York, 2005.
-
(2005)
Modern Multidimensional Scaling: Theory and Applications
-
-
Borg, I.1
Groenen, P.J.F.2
-
7
-
-
76549100532
-
A preconditioned Newton algorithm for the nearest correlation matrix
-
R. Borsdorf and N. J. Higham, A preconditioned Newton algorithm for the nearest correlation matrix, IMA J. Numer. Anal., 94 (2010), pp. 94-107.
-
(2010)
IMA J. Numer. Anal.
, vol.94
, pp. 94-107
-
-
Borsdorf, R.1
Higham, N.J.2
-
8
-
-
33646249113
-
Least-squares covariance matrix adjustment
-
S. Boyd and L. Xiao, Least-squares covariance matrix adjustment, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 532-546.
-
(2005)
SIAM J. Matrix Anal. Appl.
, vol.27
, pp. 532-546
-
-
Boyd, S.1
Xiao, L.2
-
9
-
-
0038485144
-
Analysis of nonsmooth symmetric-matrix-valued functions with applications to semidefinite complementarity problems
-
X. Chen, H. Qi, and P. Tseng, Analysis of nonsmooth symmetric-matrix- valued functions with applications to semidefinite complementarity problems, SIAM J. Optim., 13 (2003), pp. 960-985.
-
(2003)
SIAM J. Optim.
, vol.13
, pp. 960-985
-
-
Chen, X.1
Qi, H.2
Tseng, P.3
-
10
-
-
58049197110
-
Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming
-
Z. X. Chan and D. Sun, Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming, SIAM J. Optim., 19 (2008), pp. 370-396.
-
(2008)
SIAM J. Optim.
, vol.19
, pp. 370-396
-
-
Chan, Z.X.1
Sun, D.2
-
12
-
-
0003825410
-
-
2nd ed., Chapman and Hall/CRC, Boca Raton, FL
-
T. F. Cox and M. A. A. Cox, Multidimensional Scaling, 2nd ed., Chapman and Hall/CRC, Boca Raton, FL, 2001.
-
(2001)
Multidimensional Scaling
-
-
Cox, T.F.1
Cox, M.A.A.2
-
15
-
-
84948499836
-
An algorithm for restricted least squares regression
-
R. L. Dykstra, An algorithm for restricted least squares regression, J. Amer. Statist. Assoc., 78 (1983), pp. 839-842.
-
(1983)
J. Amer. Statist. Assoc.
, vol.78
, pp. 839-842
-
-
Dykstra, R.L.1
-
16
-
-
84862639933
-
Euclidean distance matrix completion problems
-
H.-R. Fang and D. P. O'Leary, Euclidean distance matrix completion problems, Optim. Methods Softw., 27 (2012), pp. 695-717.
-
(2012)
Optim. Methods Softw.
, vol.27
, pp. 695-717
-
-
Fang, H.-R.1
O'Leary, D.P.2
-
17
-
-
0001886656
-
A cyclic projection algorithm via duality
-
N. Gaffke and R. Mathar, A cyclic projection algorithm via duality, Metrika, 36 (1989), pp. 29-54.
-
(1989)
Metrika
, vol.36
, pp. 29-54
-
-
Gaffke, N.1
Mathar, R.2
-
18
-
-
84862928928
-
-
Technical Report, Department of Mathematics, National University of Singapore, Singapore
-
Y. Gao and D. F. Sun, A Majorized Penalty Approach for Calibrating Rank Constrained Correlation Matrix Problems, Technical Report, Department of Mathematics, National University of Singapore, Singapore, 2010.
-
(2010)
A Majorized Penalty Approach for Calibrating Rank Constrained Correlation Matrix Problems
-
-
Gao, Y.1
Sun, D.F.2
-
19
-
-
0000771519
-
An alternating projection algorithm for computing the nearest Euclidean distance matrix
-
W. Glunt, T. L. Hayden, S. Hong, and J. Wells, An alternating projection algorithm for computing the nearest Euclidean distance matrix, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 589-600.
-
(1990)
SIAM J. Matrix Anal. Appl.
, vol.11
, pp. 589-600
-
-
Glunt, W.1
Hayden, T.L.2
Hong, S.3
Wells, J.4
-
20
-
-
0025986584
-
The embedding problem for predistance matrices
-
W. Glunt, T. L. Hayden, and W.-M. Liu, The embedding problem for predistance matrices, Bull. Math. Biol., 53 (1991), pp. 769-796.
-
(1991)
Bull. Math. Biol.
, vol.53
, pp. 769-796
-
-
Glunt, W.1
Hayden, T.L.2
Liu, W.-M.3
-
21
-
-
0000922470
-
Molecular conformations from distance matrices
-
W. Glunt, T. L. Hayden, and R. Raydan, Molecular conformations from distance matrices, J. Comput. Chem., 14 (1993), pp. 114-120.
-
(1993)
J. Comput. Chem.
, vol.14
, pp. 114-120
-
-
Glunt, W.1
Hayden, T.L.2
Raydan, R.3
-
22
-
-
84986533367
-
Preconditioners for distance matrix algorithms
-
W. Glunt, T. L. Hayden, and R. Raydan, Preconditioners for distance matrix algorithms, J. Comput. Chem., 15 (1994), pp. 227-232.
-
(1994)
J. Comput. Chem.
, vol.15
, pp. 227-232
-
-
Glunt, W.1
Hayden, T.L.2
Raydan, R.3
-
23
-
-
0038087036
-
Properties of Euclidean and non-Euclidean distance matrices
-
J. C. Gower, Properties of Euclidean and non-Euclidean distance matrices, Linear Algebra Appl., 67 (1985), pp. 81-97.
-
(1985)
Linear Algebra Appl.
, vol.67
, pp. 81-97
-
-
Gower, J.C.1
-
24
-
-
0023860607
-
A successive projection method
-
S. P. Han, A successive projection method, Math. Programming, 40 (1988), pp. 1-14.
-
(1988)
Math. Programming
, vol.40
, pp. 1-14
-
-
Han, S.P.1
-
25
-
-
0041904419
-
Approximation by matrices positive semidefinite on a subspace
-
T. L. Hayden and J. Wells, Approximation by matrices positive semidefinite on a subspace, Linear Algebra Appl., 109 (1988), pp. 115-130.
-
(1988)
Linear Algebra Appl.
, vol.109
, pp. 115-130
-
-
Hayden, T.L.1
Wells, J.2
-
26
-
-
44949291374
-
The cone of distance matrices
-
T. L. Hayden, J. Wells, W.-M. Liu, and P. Tarazaga, The cone of distance matrices, Linear Algebra Appl., 144 (1991), pp. 153-169.
-
(1991)
Linear Algebra Appl.
, vol.144
, pp. 153-169
-
-
Hayden, T.L.1
Wells, J.2
Liu, W.-M.3
Tarazaga, P.4
-
27
-
-
0000135303
-
Methods of conjugate gradients for solving linear systems
-
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand., 49 (1952), pp. 409-436.
-
(1952)
J. Res. Nat. Bur. Stand.
, vol.49
, pp. 409-436
-
-
Hestenes, M.R.1
Stiefel, E.2
-
28
-
-
0344153904
-
Computing the nearest correlation matrix - A problem from finance
-
N. J. Higham, Computing the nearest correlation matrix - a problem from finance, IMA J. Numer. Anal., 22 (2002), pp. 329-343.
-
(2002)
IMA J. Numer. Anal.
, vol.22
, pp. 329-343
-
-
Higham, N.J.1
-
29
-
-
84867309078
-
An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP
-
K. Jiang, D. Sun, and K.-C. Toh, An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP, SIAM J. Optim., 22 (2012), pp. 1042-1064.
-
(2012)
SIAM J. Optim.
, vol.22
, pp. 1042-1064
-
-
Jiang, K.1
Sun, D.2
Toh, K.-C.3
-
30
-
-
84924072976
-
Euclidean distance matrices and applications
-
M. Anjos and J. Lasserre, eds., Springer, New York
-
N. Krislock and H.Wolkowicz, Euclidean distance matrices and applications, in Handbook on Semidefinite, Conic and Polynomial Optimization, M. Anjos and J. Lasserre, eds., Springer, New York, 2012, pp. 879-914.
-
(2012)
Handbook on Semidefinite, Conic and Polynomial Optimization
, pp. 879-914
-
-
Krislock, N.1
Wolkowicz, H.2
-
31
-
-
14544268199
-
A dual approach to semidefinite least-squares problems
-
J. Malick, A dual approach to semidefinite least-squares problems, SIAM J. Matrix Anal. Appl., 26 (2004), pp. 272-284.
-
(2004)
SIAM J. Matrix Anal. Appl.
, vol.26
, pp. 272-284
-
-
Malick, J.1
-
32
-
-
33746133967
-
Clarke generalized Jacobian of the projection onto the cone of positive semidefinite matrices
-
J. Malick and H. S. Sendov, Clarke generalized Jacobian of the projection onto the cone of positive semidefinite matrices, Set-Valued Anal., 14 (2006), pp. 273-293.
-
(2006)
Set-Valued Anal.
, vol.14
, pp. 273-293
-
-
Malick, J.1
Sendov, H.S.2
-
34
-
-
0001036636
-
Smoothing and interpolation in a convex subset of a Hilbert space
-
C. A. Micchelli and F. I. Utreras, Smoothing and interpolation in a convex subset of a Hilbert space, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 728-746.
-
(1988)
SIAM J. Sci. Stat. Comput.
, vol.9
, pp. 728-746
-
-
Micchelli, C.A.1
Utreras, F.I.2
-
35
-
-
34548480020
-
A method of solving a convex programming problem with convergence rate O(1/k2)
-
Y. Nesterov, A method of solving a convex programming problem with convergence rate O(1/k2), Soviet Math. Dokl., 27 (1983), pp. 372-376.
-
(1983)
Soviet Math. Dokl.
, vol.27
, pp. 372-376
-
-
Nesterov, Y.1
-
36
-
-
0031236591
-
Molecular modeling of proteins and mathematical prediction of protein structure
-
A. Neumaier, Molecular modeling of proteins and mathematical prediction of protein structure, SIAM Rev., 39 (1997), pp. 407-460.
-
(1997)
SIAM Rev.
, vol.39
, pp. 407-460
-
-
Neumaier, A.1
-
37
-
-
58049191300
-
Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming
-
H.-D. Qi, Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming, Linear Algebra Appl., 430 (2009), pp. 1151-1164.
-
(2009)
Linear Algebra Appl.
, vol.430
, pp. 1151-1164
-
-
Qi, H.-D.1
-
38
-
-
34247364678
-
A quadratically convergent Newton method for computing the nearest correlation matrix
-
H. Qi and D. Sun, A quadratically convergent Newton method for computing the nearest correlation matrix, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 360-385.
-
(2006)
SIAM J. Matrix Anal. Appl.
, vol.28
, pp. 360-385
-
-
Qi, H.1
Sun, D.2
-
39
-
-
0027543961
-
A nonsmooth version of Newton's method
-
L. Qi and J. Sun, A nonsmooth version of Newton's method, Math. Programming, 58 (1993), pp. 353-367.
-
(1993)
Math. Programming
, vol.58
, pp. 353-367
-
-
Qi, L.1
Sun, J.2
-
40
-
-
84877352662
-
-
Tech. Report, School of Mathematics, University of Southampton, Southampton, UK
-
H.-D. Qi and X. M. Yuan, Computing the Nearest Euclidean Distance Matrix with Low Embedding Dimensions, Tech. Report, School of Mathematics, University of Southampton, Southampton, UK, 2012.
-
(2012)
Computing the Nearest Euclidean Distance Matrix with Low Embedding Dimensions
-
-
Qi, H.-D.1
Yuan, X.M.2
-
41
-
-
0003350183
-
Conjugate duality and optimization CBMS-NSF reg
-
SIAM, Philadelphia
-
R. T. Rockafellar, Conjugate Duality and Optimization, CBMS-NSF Reg. Conf. Ser. Appl. Math. 16, SIAM, Philadelphia, 1974.
-
(1974)
Conf. Ser. Appl. Math.
, vol.16
-
-
Rockafellar, R.T.1
-
42
-
-
0001203499
-
Remarks to Maurice Fréchet's article "sur la définition axiomatique d'une classe d'espace vectoriels distanciés vectoriellement applicables sur l'espace de Hilbert,"
-
I. J. Schoenberg, Remarks to Maurice Fréchet's article "Sur la définition axiomatique d'une classe d'espace vectoriels distanciés vectoriellement applicables sur l'espace de Hilbert," Ann. Math., 36 (1935), pp. 724-732.
-
(1935)
Ann. Math.
, vol.36
, pp. 724-732
-
-
Schoenberg, I.J.1
-
43
-
-
33746089809
-
The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications
-
D. F. Sun, The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications, Math. Oper. Res., 31 (2006), pp. 761-776.
-
(2006)
Math. Oper. Res.
, vol.31
, pp. 761-776
-
-
Sun, D.F.1
-
44
-
-
0036474487
-
Semismooth matrix valued functions
-
D. F. Sun and J. Sun, Semismooth matrix valued functions, Math. Oper. Res., 27 (2002), pp. 150-169.
-
(2002)
Math. Oper. Res.
, vol.27
, pp. 150-169
-
-
Sun, D.F.1
Sun, J.2
-
45
-
-
34547439695
-
An inexact path-following algorithm for convex quadratic SDP
-
K. C. Toh, An inexact path-following algorithm for convex quadratic SDP, Math. Programming, 112 (2008), pp. 221-254.
-
(2008)
Math. Programming
, vol.112
, pp. 221-254
-
-
Toh, K.C.1
-
46
-
-
72549116352
-
-
Tech. report, University of Washington, Seattle, WA
-
P. Tseng, On Accelerated Proximal Gradient Methods for Convex-Concave Optimization, Tech. report, University of Washington, Seattle, WA, 2008.
-
(2008)
On Accelerated Proximal Gradient Methods for Convex-Concave Optimization
-
-
Tseng, P.1
-
47
-
-
0002361037
-
Discussion of a set of points in terms of their mutual distances
-
G. Young and A. S. Householder, Discussion of a set of points in terms of their mutual distances, Psychometrika, 3 (1938), pp. 19-22.
-
(1938)
Psychometrika
, vol.3
, pp. 19-22
-
-
Young, G.1
Householder, A.S.2
|