-
1
-
-
0000569649
-
Random walk on finite groups and rapidly mixing Markov chains
-
Lecture Notes in Math. 986, Springer-Verlag, New York
-
D. Aldous, Random walk on finite groups and rapidly mixing Markov chains, in Séminaire de Probabilités XVII, Lecture Notes in Math. 986, Springer-Verlag, New York, 1983, pp. 243-297.
-
(1983)
Séminaire de Probabilités XVII
, pp. 243-297
-
-
Aldous, D.1
-
2
-
-
0003169116
-
Interior point methods in semidefinite programming with applications to combinatorial optimization
-
F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization, Siam J. Optim., 5 (1995), pp. 13-51.
-
(1995)
Siam J. Optim.
, vol.5
, pp. 13-51
-
-
Alizadeh, F.1
-
3
-
-
11344277162
-
-
F. Alizadeh, J.-P. A. Haeberly, M. V. Nayakkankuppam, M. L. Overton, and S. Schmieta, SDPpack: A Package for Semidefinite-Quadratic-Linear Programming, 1997.
-
(1997)
SDPpack: A Package for Semidefinite-Quadratic-Linear Programming
-
-
Alizadeh, F.1
Haeberly, J.-P.A.2
Nayakkankuppam, M.V.3
Overton, M.L.4
Schmieta, S.5
-
4
-
-
0242710969
-
Introduction to Markov Chains, with Special Emphasis on Rapid Mixing
-
Vieweg, Weisbaden, Germany
-
E. Behrends, Introduction to Markov Chains, with Special Emphasis on Rapid Mixing, Adv. Lectures Math., Vieweg, Weisbaden, Germany, 2000.
-
(2000)
Adv. Lectures Math.
-
-
Behrends, E.1
-
5
-
-
0003878614
-
-
MPS/SIAM Ser. Optim. 2, SIAM, Philadelphia
-
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS/SIAM Ser. Optim. 2, SIAM, Philadelphia, 2001.
-
(2001)
Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
-
-
Ben-Tal, A.1
Nemirovski, A.2
-
6
-
-
0039772219
-
Solving large-scale sparse semidefinite programs for combinatorial optimization
-
S. J. Benson, Y. Ye, and X. Zhang, Solving large-scale sparse semidefinite programs for combinatorial optimization, Siam J. Optim., 10 (2000), pp. 443-461.
-
(2000)
Siam J. Optim.
, vol.10
, pp. 443-461
-
-
Benson, S.J.1
Ye, Y.2
Zhang, X.3
-
7
-
-
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
-
8
-
-
0041386088
-
A geometric interpretation of the Metropolis-Hastings algorithm
-
L. Billera and P. Diaconis, A geometric interpretation of the Metropolis-Hastings algorithm, Statist. Sci., 16 (2001), pp. 335-339.
-
(2001)
Statist. Sci.
, vol.16
, pp. 335-339
-
-
Billera, L.1
Diaconis, P.2
-
10
-
-
29844451677
-
Symmetry analysis of reversible Markov chains
-
to appear; available online from
-
S. Boyd, P. Diaconis, P. A. Parrilo, and L. Xiao, Symmetry analysis of reversible Markov chains, Internet Math., to appear; available online from http://www.stanford.edu/~boyd/symmetry.html.
-
Internet Math.
-
-
Boyd, S.1
Diaconis, P.2
Parrilo, P.A.3
Xiao, L.4
-
11
-
-
11344264478
-
Fastest mixing Markov chain on a path
-
to appear; available online from
-
S. Boyd, P. Diaconis, J. Sun, and L. Xiao, Fastest mixing Markov chain on a path, Amer. Math. Monthly, to appear; available online from http://www.stanford.edu/~boyd/fmmc_path.html.
-
Amer. Math. Monthly
-
-
Boyd, S.1
Diaconis, P.2
Sun, J.3
Xiao, L.4
-
12
-
-
0004055894
-
-
Cambridge University Press, Cambridge, UK, available online from
-
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004; available online from http:// www.stanford.edu/~boyd/cvxbook.html.
-
(2004)
Convex Optimization
-
-
Boyd, S.1
Vandenberghe, L.2
-
13
-
-
0003618624
-
Markov Chains, Gibbs Fields, Monte Carlo Simulation and Queues
-
Springer-Verlag, Berlin, Heidelberg
-
P. Brémaud, Markov Chains, Gibbs Fields, Monte Carlo Simulation and Queues, Texts Appl. Math., Springer-Verlag, Berlin, Heidelberg, 1999.
-
(1999)
Texts Appl. Math.
-
-
Brémaud, P.1
-
15
-
-
0016624432
-
The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices
-
J. Cullum, W. E. Donath, and P. Wolfe, The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices, Math. Programming Stud., 3 (1975), pp. 35-55.
-
(1975)
Math. Programming Stud.
, vol.3
, pp. 35-55
-
-
Cullum, J.1
Donath, W.E.2
Wolfe, P.3
-
17
-
-
0001874271
-
Rectangular arrays with fixed margins
-
D. Aldous et al., eds., Springer-Verlag, New York
-
P. Diaconis and A. Gangolli, Rectangular arrays with fixed margins in Discrete Probability and Algorithms, D. Aldous et al., eds., Springer-Verlag, New York, 1995, pp. 15-42.
-
(1995)
Discrete Probability and Algorithms
, pp. 15-42
-
-
Diaconis, P.1
Gangolli, A.2
-
18
-
-
0030487036
-
Logarithmic Sobolev inequalities for finite Markov chains
-
P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequalities for finite Markov chains, Ann. Appl. Probab., 6 (1996), pp. 695-750.
-
(1996)
Ann. Appl. Probab.
, vol.6
, pp. 695-750
-
-
Diaconis, P.1
Saloff-Coste, L.2
-
19
-
-
0032136909
-
What do we know about the Metropolis algorithms?
-
P. Diaconis and L. Saloff-Coste, What do we know about the Metropolis algorithms?, J. Comput. System Sci., 57 (1998), pp. 20-36.
-
(1998)
J. Comput. System Sci.
, vol.57
, pp. 20-36
-
-
Diaconis, P.1
Saloff-Coste, L.2
-
20
-
-
0002740591
-
Geometric bounds for eigenvalues of Markov chains
-
P. Diaconis and D. Stroock, Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Probab., 1 (1991), pp. 36-61.
-
(1991)
Ann. Appl. Probab.
, vol.1
, pp. 36-61
-
-
Diaconis, P.1
Stroock, D.2
-
21
-
-
0032387555
-
Algebraic algorithms for sampling from conditional distributions
-
P. Diaconis and B. Sturmfels, Algebraic algorithms for sampling from conditional distributions, Ann. Statist., 26 (1998), pp. 363-397.
-
(1998)
Ann. Statist.
, vol.26
, pp. 363-397
-
-
Diaconis, P.1
Sturmfels, B.2
-
22
-
-
84947796534
-
Engineering diffusive load balancing algorithms using experiments
-
Lecture Notes in Comput. Sci. 1253, Springer-Verlag, Berlin
-
R. Diekmann, S. Muthukrishnan, and M. V. Nayakkankuppam, Engineering diffusive load balancing algorithms using experiments, in Solving Irregularly Structured Problems in Parallel, Lecture Notes in Comput. Sci. 1253, Springer-Verlag, Berlin, 1997, pp. 111-122.
-
(1997)
Solving Irregularly Structured Problems in Parallel
, pp. 111-122
-
-
Diekmann, R.1
Muthukrishnan, S.2
Nayakkankuppam, M.V.3
-
23
-
-
0002236459
-
Logarithmic Sobolev inequalities and contractivity properties of semigroups
-
Lecture Notes in Math. 1563, Springer-Verlag, Berlin
-
L. Gross, Logarithmic Sobolev inequalities and contractivity properties of semigroups, in Dirichlet Forms (Varenna, 1992), Lecture Notes in Math. 1563, Springer-Verlag, Berlin, 1993, pp. 54-88.
-
(1993)
Dirichlet Forms (Varenna, 1992)
, pp. 54-88
-
-
Gross, L.1
-
24
-
-
77956890234
-
Monte Carlo sampling methods using Markov chains and their applications
-
W. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57 (1970), pp. 97-109.
-
(1970)
Biometrika
, vol.57
, pp. 97-109
-
-
Hastings, W.1
-
25
-
-
0034415006
-
A spectral bundle method for semidefinite programming
-
C. Helmberg and F. Rendl, A spectral bundle method for semidefinite programming, Siam J. Optim., 10 (2000), pp. 673-696.
-
(2000)
Siam J. Optim.
, vol.10
, pp. 673-696
-
-
Helmberg, C.1
Rendl, F.2
-
29
-
-
0024904712
-
Approximating the permanent
-
M. Jerrum and A. Sinclair, Approximating the permanent, Siam J. Comput., 18 (1989), pp. 1149-1178.
-
(1989)
Siam J. Comput.
, vol.18
, pp. 1149-1178
-
-
Jerrum, M.1
Sinclair, A.2
-
30
-
-
84947909878
-
A semidefinite bound for mixing tares of Markov chains
-
Lecture Notes in Comput. Sci. 1084, Springer-Verlag, Berlin
-
N. Kahale, A semidefinite bound for mixing tares of Markov chains, in Proceedings of the 5th Integer Programming and Combinatorial Optimization Conference, Lecture Notes in Comput. Sci. 1084, Springer-Verlag, Berlin, 1996, pp. 190-203.
-
(1996)
Proceedings of the 5th Integer Programming and Combinatorial Optimization Conference
, pp. 190-203
-
-
Kahale, N.1
-
32
-
-
0030304775
-
Convex analysis on the Hermitian matrices
-
A. S. Lewis, Convex analysis on the Hermitian matrices, Siam J. Optim., 6 (1996), pp. 164-177.
-
(1996)
Siam J. Optim
, vol.6
, pp. 164-177
-
-
Lewis, A.S.1
-
33
-
-
0003111058
-
Nonsmooth analysis of eigenvalues
-
A. S. Lewis, Nonsmooth analysis of eigenvalues, Math. Programming, 84 (1999), pp. 1-24.
-
(1999)
Math. Programming
, vol.84
, pp. 1-24
-
-
Lewis, A.S.1
-
34
-
-
0042602157
-
Eigenvalue optimization
-
A. S. Lewis and M. L. Overton, Eigenvalue optimization, Acta Numer., 5 (1996), pp. 149-190.
-
(1996)
Acta Numer.
, vol.5
, pp. 149-190
-
-
Lewis, A.S.1
Overton, M.L.2
-
35
-
-
0004182828
-
Monte Carlo Strategies in Scientific Computing
-
Springer Ser. Statist., Springer-Verlag, New York
-
J. Liu, Monte Carlo Strategies in Scientific Computing, Springer Ser. Statist., Springer-Verlag, New York, 2001.
-
(2001)
-
-
Liu, J.1
-
36
-
-
5744249209
-
Equations of state calculations by fast computing machines
-
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, Ande. Teller, Equations of state calculations by fast computing machines, J. Chem. Phys., 21 (1953), pp. 1087-1092.
-
(1953)
J. Chem. Phys.
, vol.21
, pp. 1087-1092
-
-
Metropolis, N.1
Rosenbluth, A.2
Rosenbluth, M.3
Teller, A.4
Teller, A.5
-
37
-
-
0034547467
-
A bundle method for efficiently solving large structured linear matrix inequalities
-
Chicago, IL
-
S. A. Miller and R. S. Smith, A bundle method for efficiently solving large structured linear matrix inequalities, in Proceedings of the American Control Conference, Chicago, IL, 2000, pp. 1405-1409.
-
(2000)
Proceedings of the American Control Conference
, pp. 1405-1409
-
-
Miller, S.A.1
Smith, R.S.2
-
38
-
-
0003254248
-
Interior-Point Polynomial Algorithms in Convex Programming
-
Siam, Philadelphia
-
Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming, Siam Stud. Appl. Math., Siam, Philadelphia, 1994.
-
(1994)
Siam Stud. Appl. Math.
-
-
Nesterov, Y.1
Nemirovskii, A.2
-
39
-
-
0003181133
-
Large-scale optimization of eigenvalues
-
M. L. Overton, Large-scale optimization of eigenvalues, Siam J. Optim., 2 (1992), pp. 88-120.
-
(1992)
Siam J. Optim.
, vol.2
, pp. 88-120
-
-
Overton, M.L.1
-
40
-
-
34250080273
-
Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices
-
M. L. Overton and R. S. Womersley, Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices, Math. Programming, 62 (1993), pp. 321-357.
-
(1993)
Math. Programming
, vol.62
, pp. 321-357
-
-
Overton, M.L.1
Womersley, R.S.2
-
41
-
-
0003668665
-
The Symmetric Eigenvalue Problem
-
Prentice-Hall, Englewood Cliffs, NJ
-
B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.
-
(1980)
-
-
Parlett, B.N.1
-
42
-
-
11344286377
-
Fastest Mixing Markov Chain on Graphs with Symmetries
-
manuscript in preparation
-
P. A. Parrilo, L. Xiao, S. Boyd, and P. Diaconis, Fastest Mixing Markov Chain on Graphs with Symmetries, manuscript in preparation, 2004.
-
(2004)
-
-
Parrilo, P.A.1
Xiao, L.2
Boyd, S.3
Diaconis, P.4
-
43
-
-
0004267646
-
Convex Analysis
-
Princeton University Press, Princeton, NJ
-
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
-
(1970)
-
-
Rockafellar, R.T.1
-
44
-
-
0000926886
-
Convergence rates for Markov chains
-
J. S. Rosenthal, Convergence rates for Markov chains, Siam Rev., 37 (1995), pp. 387-405.
-
(1995)
Siam Rev.
, vol.37
, pp. 387-405
-
-
Rosenthal, J.S.1
-
45
-
-
0003521777
-
Numerical Methods for Large Eigenvalue Problems
-
Manchester University Press, Manchester, UK
-
Y. Saad, Numerical Methods for Large Eigenvalue Problems, Manchester University Press, Manchester, UK, 1992.
-
(1992)
-
-
Saad, Y.1
-
46
-
-
32044432496
-
Semidefinite programming page
-
Website maintained by C. Helmberg
-
Semidefinite programming page, http://www-user.tu-chemnitz.de/ ~helmberg/semidef.html. Website maintained by C. Helmberg.
-
-
-
-
47
-
-
0003995427
-
Minimization Methods for Non-differentiable Functions
-
Springer-Verlag, Berlin
-
N. Z. Shor, Minimization Methods for Non-differentiable Functions, Springer Ser. Comput. Math., Springer-Verlag, Berlin, 1985.
-
(1985)
Springer Ser. Comput. Math.
-
-
Shor, N.Z.1
-
48
-
-
84971804758
-
Improved bounds for mixing rates of Markov chains and multicommodity flow
-
A. Sinclair, Improved bounds for mixing rates of Markov chains and multicommodity flow, Combin. Probab. Comput., 1 (1992), pp. 351-370.
-
(1992)
Combin. Probab. Comput.
, vol.1
, pp. 351-370
-
-
Sinclair, A.1
-
49
-
-
0003445019
-
Algorithms for Random Generation and Counting: A Markov Chain Approach
-
Birkhäuser Boston, Boston
-
A. Sinclair, Algorithms for Random Generation and Counting: A Markov Chain Approach, Birkhäuser Boston, Boston, 1993.
-
(1993)
-
-
Sinclair, A.1
-
50
-
-
0002236462
-
Logarithmic Sobolev inequalities for Gibbs states
-
Lecture Notes in Math. 1563, Springer-Verlag, Berlin
-
D. Stroock, Logarithmic Sobolev inequalities for Gibbs states, in Dirichlet Forms (Varenna, 1992), Lecture Notes in Math. 1563, Springer-Verlag, Berlin, 1993, pp. 194-228.
-
(1993)
Dirichlet Forms (Varenna, 1992)
, pp. 194-228
-
-
Stroock, D.1
-
51
-
-
0033296299
-
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
-
11-12, special issue on Interior Point Methods (CD supplement with software)
-
J. F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw., 11-12 (1999), pp. 625-653; special issue on Interior Point Methods (CD supplement with software).
-
Optim. Methods Softw. 1999
, pp. 625-653
-
-
Sturm, J.F.1
-
52
-
-
0000920501
-
Semidefinite optimization
-
M. Todd, Semidefinite optimization, Acta Numer., 10 (2001), pp. 515-560.
-
(2001)
Acta Numer.
, vol.10
, pp. 515-560
-
-
Todd, M.1
-
53
-
-
0033295027
-
SDPT3: A Matlab software package for semidefinite programming, version 2.1
-
K. C. Toh, M. J. Todd, and R. H. Tutuncu, SDPT3: A Matlab software package for semidefinite programming, version 2.1, Optim. Methods Softw., 11 (1999), pp. 545-581.
-
(1999)
Optim. Methods Softw.
, vol.11
, pp. 545-581
-
-
Toh, K.C.1
Todd, M.J.2
Tutuncu, R.H.3
-
54
-
-
0030106462
-
Semidefinite programming
-
L. Vandenberghe and S. Boyd, Semidefinite programming, Siam Rev., 38 (1996), pp. 49-95.
-
(1996)
Siam Rev.
, vol.38
, pp. 49-95
-
-
Vandenberghe, L.1
Boyd, S.2
-
55
-
-
0003395487
-
-
Kluwer Academic Publishers, Dordrecht, The Netherlands
-
H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds., Handbook of Semidefinite Programming, Theory, Algorithms, and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
-
(2000)
Handbook of Semidefinite Programming, Theory, Algorithms, and Applications
-
-
Wolkowicz, H.1
Saigal, R.2
Vandenberghe, L.3
-
56
-
-
0003857247
-
SDPSOL: A Parser/Solver for Semidefinite Programming and Determinant Maximization Problems with Matrix Structure. User's Guide Version Beta
-
Stanford University, Stanford, CA
-
S.-P. Wu and S. Boyd, SDPSOL: A Parser/Solver for Semidefinite Programming and Determinant Maximization Problems with Matrix Structure. User's Guide, Version Beta, Stanford University, Stanford, CA, 1996.
-
(1996)
-
-
Wu, S.-P.1
Boyd, S.2
-
57
-
-
0004212716
-
Interior Point Algorithms: Theory and Analysis
-
Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, New York
-
Y. Ye, Interior Point Algorithms: Theory and Analysis, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, New York, 1997.
-
(1997)
-
-
Ye, Y.1
|