-
1
-
-
0041629678
-
The real positive definite completion problem for a simple cycle
-
BARRETT, W., JOHNSON, C. R., AND TARAZAGA, P. The real positive definite completion problem for a simple cycle. Linear Algebra Appl. 192 (1993), 3-31.
-
(1993)
Linear Algebra Appl
, vol.192
, pp. 3-31
-
-
Barrett, W.1
Johnson, C.R.2
Tarazaga, P.3
-
2
-
-
0001531895
-
Two-point step size gradient methods
-
BARZILAI, J., AND BORWEIN, J. Two-point step size gradient methods. IMA J. Numer. Anal. 8 (1988), 141-148.
-
(1988)
IMA J. Numer. Anal.
, vol.8
, pp. 141-148
-
-
Barzilai, J.1
Borwein, J.2
-
3
-
-
85014561619
-
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
-
BECK, A., AND TEBOULLE, M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 1 (2009), 183-202.
-
(2009)
SIAM J. Imaging Sci.
, vol.2
, Issue.1
, pp. 183-202
-
-
Beck, A.1
Teboulle, M.2
-
4
-
-
1542337156
-
A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
-
BURER, S., AND MONTEIRO, R. A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. 95, 2 (2003), 329-357.
-
(2003)
Math. Program.
, vol.95
, Issue.2
, pp. 329-357
-
-
Burer, S.1
Monteiro, R.2
-
5
-
-
21644465788
-
Local minima and convergence in low-rank semidefinite programming
-
BURER, S., AND MONTEIRO, R. Local minima and convergence in low-rank semidefinite programming. Math. Program. 103, 3 (2005), 427-444.
-
(2005)
Math. Program.
, vol.103
, Issue.3
, pp. 427-444
-
-
Burer, S.1
Monteiro, R.2
-
6
-
-
77951291046
-
A singular value thresholding algorithm for matrix completion
-
CAI, J.-F., CANDÈS, E. J., AND SHEN, Z. A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20, 4 (2010), 1956-1982.
-
(2010)
SIAM J. Optim.
, vol.20
, Issue.4
, pp. 1956-1982
-
-
Cai, J.-F.1
Candès, E.J.2
Shen, Z.3
-
7
-
-
71049116435
-
Exact matrix completion via convex optimization
-
CANDÈS, E. J., AND RECHT, B. Exact matrix completion via convex optimization. Found. Comput. Math. 9, 6 (2009), 717-772.
-
(2009)
Found. Comput. Math.
, vol.9
, Issue.6
, pp. 717-772
-
-
Candès, E.J.1
Recht, B.2
-
8
-
-
77951528523
-
The power of convex relaxation: Near-optimal matrix completion
-
CANDÈS, E. J., AND TAO, T. The power of convex relaxation: near-optimal matrix completion. IEEE Trans. Inform. Theory 56, 5 (2010), 2053-2080.
-
(2010)
IEEE Trans. Inform. Theory
, vol.56
, Issue.5
, pp. 2053-2080
-
-
Candès, E.J.1
Tao, T.2
-
9
-
-
85036476335
-
Complexity of quantifier elimination in the theory of algebraically closed fields
-
Springer-Verlag
-
CHISTOV, A., AND GRIGORIEV, D. Complexity of quantifier elimination in the theory of algebraically closed fields. In Proceedings of the Mathematical Foundations of Computer Science 1984 (London, UK, 1984), Springer-Verlag, pp. 17-31.
-
Proceedings of the Mathematical Foundations of Computer Science 1984 (London, UK, 1984)
, pp. 17-31
-
-
Chistov, A.1
Grigoriev, D.2
-
10
-
-
0000082954
-
Sums of squares of real polynomials
-
CHOI, M., LAM, T., AND REZNICK, B. Sums of squares of real polynomials. Symp. in Pure Math. 58, 2 (1995), 103-126.
-
(1995)
Symp. in Pure Math.
, vol.58
, Issue.2
, pp. 103-126
-
-
Choi, M.1
Lam, T.2
Reznick, B.3
-
11
-
-
0000921195
-
Initialization in semidefinite programming via a self-dual skew-symmetric embedding
-
DE KLERK, E., ROOS, C., AND TERLAKY, T. Initialization in semidefinite programming via a self-dual skew-symmetric embedding. Oper. Res. Lett. 20, 5 (1997), 213-221.
-
(1997)
Oper. Res. Lett.
, vol.20
, Issue.5
, pp. 213-221
-
-
De Klerk, E.1
Roos, C.2
Terlaky, T.3
-
13
-
-
0034853839
-
A rank minimization heuristic with application to minimum order system approximation
-
FAZEL, M., HINDI, H., AND BOYD, S. A rank minimization heuristic with application to minimum order system approximation. In Proceedings of the 2001 American Control Conference (2001), pp. 4734-4739.
-
Proceedings of the 2001 American Control Conference (2001)
, pp. 4734-4739
-
-
Fazel, M.1
Hindi, H.2
Boyd, S.3
-
14
-
-
79952483985
-
Convergence of fixed point continuation algorithms for matrix rank minimization
-
GOLDFARB, D., AND MA, S. Convergence of fixed point continuation algorithms for matrix rank minimization. Foundations of Computational Mathematics 11, 2 (2011), 183-210.
-
(2011)
Foundations of Computational Mathematics
, vol.11
, Issue.2
, pp. 183-210
-
-
Goldfarb, D.1
Ma, S.2
-
15
-
-
0004236492
-
-
third ed. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD
-
GOLUB, G. H., AND VAN LOAN, C. F. Matrix computations, third ed. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD, 1996.
-
(1996)
Matrix Computations
-
-
Golub, G.H.1
Van Loan, C.F.2
-
16
-
-
47849109874
-
Positive definite completions of partial Hermitian matrices
-
GRONE, R., JOHNSON, C. R., DE SÁ, E. M., AND WOLKOWICZ, H. Positive definite completions of partial Hermitian matrices. Linear Algebra Appl. 58 (1984), 109-124.
-
(1984)
Linear Algebra Appl
, vol.58
, pp. 109-124
-
-
Grone, R.1
Johnson, C.R.2
De Sá, E.M.3
Wolkowicz, H.4
-
17
-
-
69649095451
-
Fixed-point continuation for l1-minimization: Methodology and convergence
-
HALE, E. T., YIN, W., AND ZHANG, Y. Fixed-point continuation for l1-minimization: methodology and convergence. SIAM J. Optim. 19, 3 (2008), 1107-1130.
-
(2008)
SIAM J. Optim.
, vol.19
, Issue.3
, pp. 1107-1130
-
-
Hale, E.T.1
Yin, W.2
Zhang, Y.3
-
19
-
-
77957300831
-
Projection methods for conic feasibility problems; application to sum-of-squares decompositions
-
HENRION, D., AND MALICK, J. Projection methods for conic feasibility problems; application to sum-of-squares decompositions. Optimization Methods and Software 26, 1 (2011), 23-46.
-
(2011)
Optimization Methods and Software
, vol.26
, Issue.1
, pp. 23-46
-
-
Henrion, D.1
Malick, J.2
-
20
-
-
71149103464
-
An accelerated gradient method for trace norm minimization
-
JI, S., AND YE, J. An accelerated gradient method for trace norm minimization. In Proceedings of the 26th Annual International Conference on Machine Learning (New York, NY, USA, 2009), ICML '09, ACM, pp. 457-464.
-
Proceedings of the 26th Annual International Conference on Machine Learning (New York, NY, USA, 2009), ICML '09, ACM
, pp. 457-464
-
-
Ji, S.1
Ye, J.2
-
21
-
-
57449108073
-
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
-
KALTOFEN, E., LI, B., YANG, Z., AND ZHI, L. Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars. In ISSAC '08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation (New York, NY, USA, 2008), ACM, pp. 155-164.
-
ISSAC '08: Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation (New York, NY, USA, 2008), ACM
, pp. 155-164
-
-
Kaltofen, E.1
Li, B.2
Yang, Z.3
Zhi, L.4
-
22
-
-
77956241799
-
Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients, 2009
-
Accepted for publication in
-
KALTOFEN, E., LI, B., YANG, Z., AND ZHI, L. Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients, 2009. Accepted for publication in J. Symbolic Comput.
-
J. Symbolic Comput.
-
-
Kaltofen, E.1
Li, B.2
Yang, Z.3
Zhi, L.4
-
23
-
-
33846697416
-
On the solution of large-scale SDP problems by the modified barrier method using iterative solvers
-
Ser. B
-
KOČVARA, M., AND STINGL, M. On the solution of large-scale SDP problems by the modified barrier method using iterative solvers. Math. Program. 109, 2-3, Ser. B (2007), 413-444.
-
(2007)
Math. Program.
, vol.109
, Issue.2-3
, pp. 413-444
-
-
Kočvara, M.1
Stingl, M.2
-
25
-
-
0039506352
-
The real positive semidefinite completion problem for series-parallel graphs
-
LAURENT, M. The real positive semidefinite completion problem for series-parallel graphs. Linear Algebra Appl. 252 (1997), 347-366.
-
(1997)
Linear Algebra Appl
, vol.252
, pp. 347-366
-
-
Laurent, M.1
-
26
-
-
0035219189
-
Polynomial instances of the positive semidefinite and Euclidean distance matrix completion problems
-
LAURENT, M. Polynomial instances of the positive semidefinite and Euclidean distance matrix completion problems. SIAM J. Matrix Anal. Appl. 22, 3 (2000), 874-894.
-
(2000)
SIAM J. Matrix Anal. Appl.
, vol.22
, Issue.3
, pp. 874-894
-
-
Laurent, M.1
-
28
-
-
0030304775
-
Convex analysis on the Hermitian matrices
-
LEWIS, A. S. Convex analysis on the Hermitian matrices. SIAM J. Optim. 6, 1 (1996), 164-177.
-
(1996)
SIAM J. Optim.
, vol.6
, Issue.1
, pp. 164-177
-
-
Lewis, A.S.1
-
29
-
-
72549110327
-
Interior-point method for nuclear norm approximation with application to system identification
-
LIU, Z., AND VANDENBERGHE, L. Interior-point method for nuclear norm approximation with application to system identification. SIAM J. Matrix Anal. Appl. 31 (2009), 1235-1256.
-
(2009)
SIAM J. Matrix Anal. Appl.
, vol.31
, pp. 1235-1256
-
-
Liu, Z.1
Vandenberghe, L.2
-
31
-
-
79957968988
-
Fixed point and bregman iterative methods for matrix rank minimization
-
MA, S., GOLDFARB, D., AND CHEN, L. Fixed point and bregman iterative methods for matrix rank minimization. Math. Program. (2009), 1-33.
-
(2009)
Math. Program.
, pp. 1-33
-
-
Ma, S.1
Goldfarb, D.2
Chen, L.3
-
32
-
-
79959664874
-
The minimum-rank Gram matrix completion via fixed point continuation method
-
in Chinese
-
MA, Y. The minimum-rank Gram matrix completion via fixed point continuation method (in Chinese). Journal of Systems Science and Mathematical Sciences 30, 11 (2010), 1501-1511.
-
(2010)
Journal of Systems Science and Mathematical Sciences
, vol.30
, Issue.11
, pp. 1501-1511
-
-
Ma, Y.1
-
33
-
-
70450212537
-
Regularization methods for semidefinite programming
-
MALICK, J., POVH, J., RENDL, F., AND WIEGELE, A. Regularization methods for semidefinite programming. SIAM J. Optim. 20, 1 (2009), 336-356.
-
(2009)
SIAM J. Optim.
, vol.20
, Issue.1
, pp. 336-356
-
-
Malick, J.1
Povh, J.2
Rendl, F.3
Wiegele, A.4
-
35
-
-
17444406259
-
Smooth minimization of non-smooth functions
-
NESTEROV, Y. Smooth minimization of non-smooth functions. Math. Program. 103, 1 (2005), 127-152.
-
(2005)
Math. Program.
, vol.103
, Issue.1
, pp. 127-152
-
-
Nesterov, Y.1
-
38
-
-
36448998081
-
A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients
-
PEYRL, H., AND PARRILO, P. A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients. In ProcSNC07 (2007), pp. 207-208.
-
ProcSNC07 (2007)
, pp. 207-208
-
-
Peyrl, H.1
Parrilo, P.2
-
39
-
-
55749106047
-
Computing sum of squares decompositions with rational coefficients
-
PEYRL, H., AND PARRILO, P. Computing sum of squares decompositions with rational coefficients. Theoretical Computer Science 409 (2008), 269-281.
-
(2008)
Theoretical Computer Science
, vol.409
, pp. 269-281
-
-
Peyrl, H.1
Parrilo, P.2
-
40
-
-
0000668151
-
Zur Darstellung definiter Funktionen als Summe von Quadraten
-
PFISTER, A. Zur Darstellung definiter Funktionen als Summe von Quadraten. Inventiones Math. 4, 4 (1967), 229-236.
-
(1967)
Inventiones Math.
, vol.4
, Issue.4
, pp. 229-236
-
-
Pfister, A.1
-
41
-
-
0002241304
-
Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques
-
POURCHET, Y. Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques. Acta Arith. 19 (1971), 89-104.
-
(1971)
Acta Arith
, vol.19
, pp. 89-104
-
-
Pourchet, Y.1
-
42
-
-
0032064831
-
An algorithm for sums of squares of real polynomials
-
POWERS, V., AND WÖRMANN, T. An algorithm for sums of squares of real polynomials. J. Pure Appl. Algebra 127, 1 (1998), 99-104.
-
(1998)
J. Pure Appl. Algebra
, vol.127
, Issue.1
, pp. 99-104
-
-
Powers, V.1
Wörmann, T.2
-
43
-
-
78549288866
-
Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
-
RECHT, B., FAZEL, M., AND PARRILO, P. A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52, 3 (2010), 471-501.
-
(2010)
SIAM Rev.
, vol.52
, Issue.3
, pp. 471-501
-
-
Recht, B.1
Fazel, M.2
Parrilo, P.A.3
-
44
-
-
62949189702
-
Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization
-
RECHT, B., XU, W., AND HASSIBI, B. Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization. In CDC (2008), pp. 3065-3070.
-
CDC (2008)
, pp. 3065-3070
-
-
Recht, B.1
Xu, W.2
Hassibi, B.3
-
48
-
-
0033296299
-
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
-
STURM, J. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11/12 (1999), 625-653.
-
(1999)
Optimization Methods and Software
, vol.11-12
, pp. 625-653
-
-
Sturm, J.1
-
50
-
-
70049111607
-
On accelerated proximal gradient methods for convex-concave optimization
-
TSENG, P. On accelerated proximal gradient methods for convex-concave optimization. Submitted to SIAM J. Optim (2008).
-
(2008)
Submitted to SIAM J. Optim
-
-
Tseng, P.1
-
51
-
-
0011336092
-
Characterization of the subdifferential of some matrix norms
-
WATSON, G. A. Characterization of the subdifferential of some matrix norms. Linear Algebra Appl. 170 (1992), 33-45.
-
(1992)
Linear Algebra Appl.
, vol.170
, pp. 33-45
-
-
Watson, G.A.1
-
52
-
-
77955666600
-
A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation
-
WEN, Z., YIN, W., GOLDFARB, D., AND ZHANG, Y. A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. SIAM J. Sci. Comput. 32, 4 (2010), 1832-1857.
-
(2010)
SIAM J. Sci. Comput.
, vol.32
, Issue.4
, pp. 1832-1857
-
-
Wen, Z.1
Yin, W.2
Goldfarb, D.3
Zhang, Y.4
-
53
-
-
77951274410
-
A Newton-CG augmented Lagrangian method for semidefinite programming
-
ZHAO, X.-Y., SUN, D., AND TOH, K.-C. A Newton-CG augmented Lagrangian method for semidefinite programming. SIAM J. Optim. 20, 4 (2010), 1737-1765.
-
(2010)
SIAM J. Optim.
, vol.20
, Issue.4
, pp. 1737-1765
-
-
Zhao, X.-Y.1
Sun, D.2
Toh, K.-C.3
|