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ResearchGate
Preprints
 Y.J. Zhang, N. Zhang, D.F. Sun, and K.C. Toh,
A proximal point dual Newton algorithm for solving group graphical Lasso
problems,
arXiv:1906.04647, 2019.
 X.D. Li, D.F. Sun, and K.C. Toh,
An asymptotically superlinearly convergent semismooth
Newton augmented Lagrangian method for Linear Programming,
arXiv:1903.09546, 2019.
 P.P. Tang, C.J. Wang, D.F. Sun, and K.C. Toh,
A sparse semismooth Newton based proximal majorizationminimization algorithm
for nonconvex squarerootloss regression problems,
arXiv:1903.11460, 2019.
 N. Zhang, Y.J. Zhang, D.F. Sun, and K.C. Toh,
An efficient linearly convergent regularized proximal point algorithm for
fused multiple graphical Lasso problems,
arXiv:1902.06952, 2019.
 S.Y. Kim, M. Kojima, and K.C. Toh,
A geometrical analysis of a class of nonconvex conic programs for convex conic reformulations of
quadratic and polynomial optimization problems,
arXiv:1901.02179, 2019.
 X.Y. Lam, D.F Sun, and K.C. Toh,
A semiproximal augmented Lagrangian based decomposition method for primal block angular convex
composite quadratic conic programming problems,
arXiv:1812.04941, 2018.
 T.D. Quoc, L. Liang, K.C. Toh,
A new homotopy proximal variablemetric framework for composite convex minimization,
arXiv:1812.05243, 2018.
 S.L. Hu, D.F. Sun, J. Sun, and K.C. Toh,
Best nonnegative rankone approximations of tensors,
arXiv:1810.13372, 2018.
 C. Ding, D.F. Sun, J. Sun, and K.C. Toh,
Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian,
arXiv:1810.09856, 2018.
 D.F. Sun, K.C. Toh, and Y.C. Yuan,
Convex clustering: model, theoretical guarantee and efficient algorithm,
arXiv:1810.02677, 2018.
 L. Yang, J. Li, D.F. Sun, and K.C. Toh,
A fast globally linearly convergent algorithm for the computation of Wasserstein barycenters,
arXiv:1809.04249, 2018.
 L. Chen, X.D. Li, D.F. Sun, and K.C. Toh,
On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming,
arXiv:1803.10803, 2018.
 Y. Cui, D.F. Sun, and K.C. Toh,
Computing the best approximation over the intersection of a polyhedral set and the doubly nonnegative cone,
arXiv:1803.06566, 2018.
 Y. Cui, D.F. Sun and K.C. Toh,
On the asymptotic superlinear convergence of the augmented Lagrangian method
for semidefinite programming with multiple solutions,
arXiv:1610.00875, 2016.
 S.Y. Kim, M. Kojima, and K.C. Toh,
Doubly nonnegative relaxations for quadratic and polynomial optimization problems
with binary and box constraints,
preprint at Optimization Online, 2016.
Book chapters and others
 K.C. Toh,
Some numerical issues in the development of SDP algorithms, INFORMS OS Today,
Volume 8 Number 2 (2008), pp. 720.
 K.C. Toh, M.J. Todd, and R.H. Tutuncu,
On the implementation and usage of SDPT3  a Matlab software
package for semidefinitequadraticlinear programming,
version 4.0,
in Handbook on semidefinite, cone and
polynomial optimization: theory, algorithms, software and applications,
M. Anjos and J.B. Lasserre eds., Springer, 2012, pp. 715754.
Here is the
complete performance results obtained by SDPT34.0
on over 400 problems.
 X.Y. Fang and K.C. Toh,
Using a distributed SDP approach to solve simulated
protein molecular conformation problems,
in Distance Geometry: Theory, Methods, and Applications,
A. Mucherino, C. Lavor, L. Liberti, and N. Maculan eds.,
Springer, 2013, pp. 351376.
 K.F. Jiang, D.F. Sun, and K.C. Toh,
Solving nuclear norm regularized and semidefinite matrix least squares problems
with linear equality constraints,
Fields Institute Communications Volume 69, Discrete Geometry and
Optimization,
K. Bezdek, Y. Ye, and A. Deza eds., Springer, 2013, pp. 133162.
Accepted and published journal papers
2017present
 Z.Y. Lou, D.F. Sun, K.C. Toh, and N.H. Xiu,
Solving the OSCAR and SLOPE models using a semismooth Newtonbased augmented Lagrangian method,
J. Machine Learning Research,
in print, 2019.
arXiv:1803.10740.
 M.X. Lin, Y.J. Liu, D.F. Sun, and K.C. Toh,
Efficient sparse Hessian based algorithms for the clustered Lasso problem,
SIAM J. Optimization, in print, 2019.
arXiv:1808.07181.
 L. Chen, D.F. Sun, K.C. Toh, and N. Zhang,
A unified algorithmic framework of symmetric GaussSeidel decomposition based proximal ADMMs for convex
composite programming,
J. Computational Mathematics, in print, 2019.
arXiv:1812.06579.

N. Ito, S. Kim, M. Kojima, A. Takeda, and K.C. Toh,
BBCPOP: A sparse doubly nonnegative relaxation of polynomial
optimization problems with binary, box and complementarity constraints,
ACM Transactions on Mathematical Software, in print, 2019.
arXiv:1804.00761.
BBCPOP Matlab Software.
Valid lower bounds for large QAPs
computed by Hans Mittelmann using BBCPOP.

L. Chen, D.F. Sun and K.C. Toh,
Some problems on the GaussSeidel iteration method in degenerate cases,
(in Chinese)
Journal On Numerical Methods and Computer Applications, in print, 2019.
 D.F. Sun, K.C. Toh, Y.C. Yuan, and X.Y. Zhao,
SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0),
Optimization Methods and Software, in print, 2019.
arXiv:1710.10604.

X.D. Li, D.F. Sun and K.C. Toh,
On the efficient computation of a generalized Jacobian of the projector
over the Birkhoff polytope,
Mathematical Programming, in print, 2018.
arXiv:1702.05934.
Springer Nature ShareIt.

Y.J. Zhang, N. Zhang, D.F. Sun and K.C. Toh,
An efficient Hessian based algorithm for solving
largescale sparse group Lasso problems,
Mathematical Programming, in print, 2018.
arXiv:1712.05910.
Springer Nature ShareIt.

Y. Cui, D.F. Sun and K.C. Toh,
On the Rsuperlinear convergence of the KKT residuals generated by the augmented Lagrangian method for convex composite conic programming,
Mathematical Programming, in print, 2018.
arXiv:1706.08800.
Springer Nature SharedIt.

X.D. Li, D.F. Sun and K.C. Toh,
A block symmetric GaussSeidel decomposition theorem for convex composite quadratic programming and its applications,
Mathematical Programming, 175 (2019), pp. 395418.
arXiv:1703.06629.
Springer Nature SharedIt.

N. Ito, S. Kim, M. Kojima, A. Takeda, and K.C. Toh,
Equivalences and differences in conic relaxations of
combinatorial quadratic optimization problems,
J. Global Optimization, 72 (2018), pp. 619653.
Preprint at Optimization Online.
Springer Nature SharedIt.

X.D. Li, D.F. Sun and K.C. Toh,
On efficiently solving the subproblems of a levelset method for fused lasso problems,
SIAM J. Optimization, 28 (2018), pp. 18421866.
arXiv:1706.08732.
Detailed computational results in the paepr.

X.D. Li, D.F. Sun, and K.C. Toh,
QSDPNAL: A twophase augmented Lagrangian method for convex quadratic semidefinite programming,
Mathematical Programming Computation, 10 (2018), pp. 703743.
arXiv:1512.08872.
Springer Nature SharedIt.

K. Natarajan, D.J. Shi, and K.C. Toh,
Bounds for random binary quadratic programs,
SIAM J. Optimization, 28 (2018), pp. 671692.

X.D. Li, D.F. Sun, and K.C. Toh,
A highly efficient semismooth Netwon augmented Lagrangian method for solving Lasso problems,
SIAM J. Optimization, 28 (2018), pp. 433458.
arXiv:1607.05428.

Z.W. Li, L.F. Cheong, S.G. Yang, and K.C. Toh,
Simultaneous clustering and model selection: algorithm, theory and applications,
IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (2018), pp. 19641978.

X.Y. Lam, J.S. Marron, D.F. Sun, and K.C. Toh,
Fast algorithms for large scale generalized distance weighted discrimination,
J. Computational and Graphical Statistics, 27 (2018), pp. 368379.
arXiv:1604.05473.
R package.

T. Weisser, J.B. Lasserre, and K.C. Toh,
A bounded degree SOS hierarchy for large scale polynomial optimization with sparsity,
Mathematical Programming Computation, 10 (2018), pp. 132.
arXiv:1607.01151.
Springer Nature SharedIt.

C. Ding, D.F. Sun, J. Sun, and K.C. Toh,
Spectral operators of matrices,
Mathematical Programming, 168 (2018), pp. 509531.
arXiv:1401.2269.

Ethan Fang, H. Liu, K.C. Toh, W.X. Zhou,
Maxnorm optimization for robust matrix recovery,
Mathematical Programming, 167 (2018), pp. 535.
Preprint at Optimization
Online.
Springer Nature SharedIt.
 N. Arima, S.Y. Kim, M. Kojima, and K.C. Toh,
Lagrangianconic relaxations, Part I:
A unified framework and its applications to
quadratic optimization problems,
Pacific J. Optimization, 14 (2018), pp.161192.
Preprint at Optimization Online.
 N. Arima, S.Y. Kim, M. Kojima, and K.C. Toh,
Lagrangianconic relaxations, Part II:
Applications to
polynomial optimization problems,
Pacific J. Optimization, in print.
Preprint at Optimization Online.

N. Ito, A. Takeda, and K.C. Toh,
A unified formulation and fast accelerated proximal gradient method for classification,
J. Machine Learning Research, 18 (2017), article 16, pp.149.

N. Arima, S.Y. Kim, M. Kojima, and K.C. Toh,
A robust LagrangianDNN method for a class of quadratic optimizaiton
problems,
Computational Optimization and Applications, 66 (2017), pp. 453479.
Preprint at Optimization Online.

L. Chen, D.F. Sun, and K.C. Toh,
A note on the convergence of ADMM for linearly constrained convex
optimization problems,
Computational Optimization and Applications, 66 (2017), pp. 327—343.
arXiv:1507.02051
 J.B. Lasserre, K.C. Toh, and S.G. Yang,
A boundedSOShierarchy for polynomial optimization,
EURO J. Computational Optimization, 5 (2017), pp. 87117.
arXiv:1501.06126.

L. Chen, D.F. Sun, and K.C. Toh,
An efficient inexact symmetric GaussSeidel based majorized ADMM for highdimensional convex composite conic programming,
Mathematical
Programming, 161 (2017), pp. 237270.
arXiv:1506.00741.
Springer Nature SharedIt.
20142016
 D.F. Sun, K.C. Toh, and L.Q. Yang,
An efficient inexact ABCD method for least squares semidefinite programming,
SIAM J. Optimization, 26 (2016), pp. 10721100.
arXiv:1505.04278.
Detailed computational results for over 600 problems tested in the paper.
 Y. Cui, X.D. Li, D.F. Sun and K.C. Toh,
On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions,
J. Optimization Theory and Applications, 169 (2016), pp. 10131041.
arXiv:1502.00098.
Springer Nature SharedIt

M. Li, D.F. Sun, and K.C. Toh,
A majorized ADMM with indefinite proximal terms for linearly
constrained convex composite optimization,
SIAM J. Optimization, 26 (2016), pp. 922950.
arXiv:1412.1911.
 S.Y. Kim, M. Kojima, and K.C. Toh,
A LagrangianDNN relaxation: a fast method
for computing tight lower bounds for a class of quadratic optimization
problems,
Mathematical Programming, 156 (2016), pp. 161187.
 C.H. Chen, Y.J. Liu, D.F. Sun, and K.C. Toh,
A semismooth NewtonCG dual proximal point algorithm for
spectral norm approximation problems,
Mathematical Programming, 155 (2016), pp. 435470.
 X.D. Li, D.F. Sun and K.C. Toh,
A Schur complement based semiproximal ADMM for convex quadratic conic
programming and extensions
,
Mathematical Programming, 155 (2016), pp. 333373.
arXiv:1409.2679.
 L.Q. Yang, D.F. Sun, and K.C. Toh,
SDPNAL+: a majorized semismooth NewtonCG augmented Lagrangian method for
semidefinite programming with nonnegative constraints,
Mathematical Programming Computation, 7 (2015), pp. 331366.
arXiv:1406.0942.
More recent computational results (computed in Dec 2017).
Detailed computational results for over 500 problems tested in the paper (computed in May 2014).
Numerical experiments on
a variety of large scale SDPs with the matrix dimension \(n\)
up to \(9,261\) and the number of equality constraints \(m\) up to \(12,326,390\)
show that the proposed method is very efficient on certain
large SDPs. We
are also able to solve the SDP problem fap36
(with \(n = 4,110\) and \(m = 1,154,467\)) in the
Seventh DIMACS Implementation Challenge much more efficiently (in 23 hours in 2015) and
accurately than previous attempts. The approximate optimal objective value
we obtained for fap36 is 69.85, with the corresponding
solution having relative primal and dual infeasibilities, and
complementarity gap \(\langle X,S\rangle\) all less than 1e6.
 D.F. Sun, K.C. Toh and L.Q. Yang,
A convergent 3block semiproximal alternating direction method of multipliers for
conic programming with 4type constraints,
SIAM J. Optimization, 25 (2015), pp. 882915.
arXiv:1404.5378.
Detailed computational results for over 400 problems tested in the paper.
Supplementary note:
more detailed comparison between the performance of our algorithm
and various variants of ADMMs.
 M. Li, D.F. Sun, and K.C. Toh,
A convergent 3block semiproximal ADMM for convex minimization with one strongly convex block,
Asia Pacific J. Operational Research, 32 (2015), 1550024.
arXiv:1410.7933.
 Y.X. Wang, C.M. Lee, L.F. Cheong, and K.C. Toh,
Practical matrix completion and corruption recovery
using proximal alternating robust subspace minimization,
International J. of Computer Vision,
111 (2015), pp. 315344.
arXiv:1309.1539.
 C. Tang, K.K. Phoon, and K.C. Toh,
Effect of footing width on Ny and failure envelope of eccentrically and obliquely loaded strip footings on sand,
Canadian Geotechnical Journal, 52 (2015), pp. 694707.
 J. Peng, T. Zhu, H. Luo, and K.C. Toh,
Semidefinite relaxation of
quadratic assignment problems based on nonredundant
matrix splitting,
Computational Optimization and Applications, 60 (2015), pp. 171198.
 K.F. Jiang, D.F. Sun, and K.C. Toh,
A partial proximal point algorithm for
nuclear norm regularized matrix least squares problems,
Mathematical Programming Computation, 6 (2014), pp. 281325.
 Z. Gong, Z.W. Shen, and K.C. Toh,
Image restoration with mixed or unknown noises,
Multiscale Modeling and Simulation, 12 (2014), pp. 458487.
 B. Wu, C. Ding, D.F. Sun, and K.C. Toh,
On the MoreauYoshida regularization of the vector knorm related functions,
SIAM J. Optimization, 24 (2014), pp. 766794.
 K. Natarajan, D.J. Shi, and K.C. Toh,
A probabilistic model for
minimax regret in combinatorial optimization,
Operations Research, 62 (2014), pp. 160181.
 C. Ding, D.F Sun and K.C. Toh,
An introduction to a class of matrix cone programming,
Mathematical Programming, 144 (2014), pp. 141179.
 C. Tang, K.K. Phoon, and K.C. Toh,
Lower bound limit analysis for seismic passive earth pressure on rigid walls,
International J. of Geomechanics,
14 (2014), 04014022.
 C. Tang, K.C. Toh, and K.K. Phoon,
Axisymmetric lower bound limit
analysis using finite elements and secondorder cone programming,
J. of
Engineering Mechanics, 140 (2014), pp. 268278.
20112013

Z.Z. Zhang, G.L. Li, K.C. Toh, and
W.K. Sung,
3D chromosome modeling with semidefinite programming
and HiC data,
J. Computational Biology, 20 (2013), pp. 831846.
 J.F. Yang, D.F. Sun, and K.C. Toh,
A proximal point algorithm for
logdeterminant optimization with group Lasso regularization,
SIAM J. Optimization, 23 (2013), pp. 857893.
 X.V. Doan, K.C. Toh, and S. Vavasis,
A proximal point algorithm for
sequential feature extraction applications,
SIAM J. Scientific Computing, 35 (2013), pp. 517540.

T.H.H. Tran, K.C. Toh, and K.K. Phoon,
Preconditioned IDR(s) iterative solver for
nonsymmetric linear system associated with
FEM analysis of shallow
foundation,
International J. for Numerical and Analytical
Methods in
Geomechanics, 37 (2013), pp. 29722986.
 K. B. Chaudhary, K.K. Phoon, and K.C. Toh,
Inexact block diagonal preconditioners to mitigate the
effects of relative differences in material stiffnesses,
International J. Geomechanics, 13 (2013), pp. 273291.
 K. B. Chaudhary, K.K. Phoon, and K.C. Toh,
Effective block diagonal preconditioners for Biot's consolidation
equations in piledraft foundations,
International J. Numerical and Analytical Methods in Geomechanics, 37 (2013), pp. 871892.
 K.F. Jiang, D.F. Sun, and K.C. Toh,
An inexact accelerated proximal gradient method for large scale
linearly constrained convex SDP,
SIAM J. Optimization, 22 (2012), pp. 10421064.
 Y.J. Liu, D.F. Sun, and K.C. Toh,
An implementable proximal point algorithmic framework
for nuclear norm minimization,
Mathematical Programming, 133 (2012), pp. 399436.
Matlab software PPApack
 X.Y. Zhao, and K.C. Toh,
Infeasible potential reduction algorithms for semidefinite programming,
Pacific J. Optimization, 8 (2012), pp. 725753.
 X. Chen, K.K. Phoon, and K.C. Toh,
Performance of zerolevel fillin preconditioning techniques for
iterative solutions in geotechnical applications,
International J. Geomechanics, 12 (2012), pp. 596605.
 Z. Shen, K.C. Toh, and S. Yun,
An accelerated proximal gradient algorithm for
frame based image restoration via the balanced approach,
SIAM J. Imaging Sciences, 4 (2011), pp. 573596.
 S. Yun, P. Tseng, and K.C. Toh,
A block coordinate gradient descent method for regularized convex
separable optimization and covariance selection,
Mathematical Programming, 129 (2011), pp. 331355.
 L. Li, and K.C. Toh,
A polynomialtime inexact primaldual infeasible
pathfollowing algorithm for convex quadratic SDP,
Pacific J. Optimization, 7 (2011), pp. 4361.
 S. Yun, and K.C. Toh,
A coordinate gradient descent method for L1regularized
convex minimization
,
Computational Optimization and Applications, 48 (2011), pp. 273307.
20082010
 K.C. Toh, and S.W. Yun
An accelerated proximal gradient
algorithm for nuclear norm regularized least squares
problems,
Pacific J. Optimization, 6 (2010), pp. 615640.
Matlab software NNLS
Numerical results suggest that our algorithm is efficient and robust
in solving largescale random matrix completion problems.
In particular, we are able to solve random matrix completion
problems with matrix dimensions up to $10^5$ each in less than
10 minutes on a modest PC.
 Lu Li and K.C. Toh
An inexact interior point method for L1regularized sparse covariance
selection,
Mathematical Programming Computation, 2 (2010), pp. 291315.
 L. Li, and K.C. Toh,
A polynomialtime inexact interiorpoint method
for convex quadratic symmetric cone programming,
J. Mathforindustry, 2 (2010), pp. 199212.
 X.W. Liu, G.Y. Zhao, and K.C. Toh,
On the implementation of a logbarrier
progressive hedging method for multistage stochastic programs,
J. of Computational and Applied Mathematics, 234 (2010), pp. 579592.
 C.J. Wang, D.F. Sun, and K.C. Toh,
Solving logdeterminant optimization problems by a NewtonCG primal
proximal point algorithm,
SIAM J. Optimization, 20 (2010), pp. 29943013.
Matlab software LogdetPPA
 X.Y. Zhao, D.F. Sun, and K.C. Toh,
A NewtonCG augmented Lagrangian method for semidefinite
programming,
SIAM J. Optimization, 20 (2010), pp. 17371765.
Matlab software SDPNAL
Numerical experiments on
a variety of large scale SDPs with the matrix dimension n
up to 4,110 and the number of equality constraints m up to 2,156,544
show that the proposed method is very efficient on certain
large SDPs. We
are also able to solve the SDP problem fap36
(with n = 4,110 and m = 1,154,467) in the
Seventh DIMACS Implementation Challenge much more
accurately than previous attempts. The approximate optimal objective value
we obtained for fap36 is 69.85, with the corresponding
solution having relative primal and dual infeasibilities, and
complementarity gap (Tr(XS)) all less than 1e6.
 N.H. Z. Leung and K.C. Toh,
An SDPbased divideandconquer algorithm for large scale noisy
anchorfree graph realization
,
SIAM J. Scientific Computing, 31 (2010), pp. 43514372.
A
movie
showing how the divideandconquer algorithm computes the
conformation of a protein molecule.
 P. Biswas, K.C. Toh, and Y. Ye,
A distributed SDP approach for large scale noisy
anchorfree graph realization with applications to
molecular conformation
,
SIAM J. Scientific Computing, 30 (2008), pp. 12511277.
 K.C. Toh,
An inexact primaldual pathfollowing algorithm for
convex quadratic SDP,
Mathematical Programming, 112 (2008),
pp. 221254.
 K.C. Toh, and K.K. Phoon,
Comparison between iterative solution of symmetric and nonsymmetric
forms of Biot's FEM equations using the generalized Jacobi
preconditioner,
International J. for Numerical and
Analytical Methods in Geomechanics, 32 (2008), pp. 11311146.
20052007
 X. Chen, K.K. Phoon, and K.C. Toh,
Partitioned versus global Krylov subspace iterative methods for
FE solution of 3D Biot's problem,
Computer Methods in Applied Mechanics and Engineering,
196 (2007), pp. 27372750.
 J.S. Chai, and K.C. Toh,
Preconditioning and iterative solution of
symmetric indefinite linear systems arising
from interior point methods for linear programming,
Computational Optimization and Applications, 36 (2007), pp. 221247.
 K.C. Toh, R.H. Tutuncu, and M.J. Todd,
Inexact primaldual pathfollowing algorithms for
a special class of convex quadratic SDP and
related problems,
Pacific J. Optimization
(special issue dedicated to Masakazu Kojima's 60th birthday),
3 (2007), pp. 135164.
 R.M. Freund, F. Ordonez, and K.C. Toh,
Behavioral measures and their correlation with IPM iteration
counts on semidefinite programming problems,
Mathematical Programming, 109 (2007), pp. 445475.
 Z. Cai and K.C. Toh,
Solving second order cone
programming via the augmented systems,
SIAM J. Optimization, 17 (2006), pp. 711737.
 P. Biswas, T.C. Liang, K.C. Toh, T.C. Wang, and Y. Ye,
Semidefinite programming approaches for sensor network
localization with noisy distance measurements,
IEEE Transactions on Automation Science
and Engineering, regular paper, 3 (2006), pp. 360371.
Matlab codes for solving small size sensor network localization
problems.
 X. Chen, K.C. Toh, and K.K. Phoon,
A modified SSOR preconditioner for sparse symmetric
indefinite linear systems of equations,
International J. Numerical Methods in Engineering,
65 (2006), pp. 785807.
 J.S. Chai and K.C. Toh,
Computation of condition numbers for linear programming
problems using Pena's method,
Optimization Methods and Software, 21 (2006), pp. 419443.
 G.L. Zhou, and K.C. Toh,
Superlinear convergence of a Newtontype algorithm for
monotone equations,
J. Optimization Theory and Applications,
125 (2005), pp. 205221.
 G.L. Zhou, K.C. Toh, and J. Sun,
Efficient algorithms for the
smallest enclosing ball problem,
Computational Optimization and Applications,
30 (2005), pp. 147160.
20022004
 K.K. Phoon, K.C. Toh, and X. Chen,
Block constrained versus generalized Jacobi preconditioners
iterative solution of largescale Biot's
FEM equations,
Computers and Structures, 82 (2004), pp. 24012411.
 K.C. Toh, K.K. Phoon, and S.H. Chan,
Block preconditioners for symmetric indefinite
linear systems,
International J. Numerical Methods in Engineering, 60 (2004),
pp. 13611381.
 S. K. Chua, K. C. Toh and G. Y. Zhao,
An analytic center cutting plane method with deep cuts
for semidefinite feasibility problems,
J. Optimization Theory and Applications, 123 (2004), pp. 291318.
 G.L. Zhou, K.C. Toh, and G.Y. Zhao,
Convergence analysis of an infeasible
interior point algorithm based on a regularized central
path for linear
complementarity problems,
Computational Optimization and Applications, 27 (2004), pp. 269283.
 K. C. Toh,
Solving large scale semidefinite programs
via an iterative solver on
the augmented systems,
SIAM J. Optimization, 14 (2004), pp. 670698.
 G.L. Zhou, and K.C. Toh,
Polynomiality of An Inexact Infeasible
Interior Point Algorithm for Semidefinite
Programming,
Mathematical Programming,
99 (2004), pp. 261282.
 Phoon, K. K., Toh, K. C., Chan, S. H., and Lee, F. H.,
Fast iterative solution of large undrained soilstructure interaction
problems,
International J. for Numerical and
Analytical Methods in Geomechanics, 27 (2003), pp. 159181.
 G.L. Zhou, K.C. Toh, and D.F. Sun,
A globally and quadratically convergent algorithm for minimizing
a sum of Euclidean norms,
J. Optimization Theory and Applications,
119 (2003), pp. 357377.
 R.H Tutuncu, K.C. Toh, and M.J. Todd,
Solving semidefinitequadraticlinear programs using
SDPT3,
Mathematical Programming,
95 (2003), pp. 189217.
 K.C. Toh, G.Y Zhao, and J. Sun,
A multiplecut analytic center cutting plane
method for semidefinite
feasibility problems,
SIAM J. Optimizaton, 12 (2002), pp. 11261146.
 J. Sun, K.C. Toh, and G.Y Zhao,
An analytic center cutting plane method for semidefinite
feasibility problems,
Mathematics of Operations Research, 27 (2002),
pp. 332346.
 K.C. Toh, and M. Kojima,
Solving some large scale semidefinite programs
via the conjugate residual method,
SIAM J. Optimization, 12 (2002), pp. 669691.
 K.C. Toh,
A note on the calculation of steplengths in
interiorpoint methods for semidefinite
programming,
Computational Optimization and Applications,
21 (2002), pp. 301310.
 K.K. Phoon, K.C. Toh, S.H. Chan, and F.H. Lee
An efficient diagonal preconditioner for
finite element solution of Biot's consolidation
equations,
International J. Numerical Methods in Engineering,
55 (2002), pp. 377400.
19992001
 A. Ron, Z.W. Shen, and K.C. Toh,
Computing the Sobolev regularity of refinable functions by the
the Arnoldi Method,
SIAM J. Matrix Analysis and Applications, 23 (2001), pp. 5776.
 K.C. Toh,
Some new search directions for primaldual interior point
methods in semidefinite programming,
SIAM J. Optimization, 11 (2000), pp. 223242.
 K.C. Toh, and L.N. Trefethen,
The Kreiss Matrix Theorem on a general complex
domain,
SIAM J. Matrix Analysis and Applications, 21 (1999), pp. 145165.
 K.C. Toh, M.J. Todd, and R.H. Tutuncu,
SDPT3  a Matlab software package for semidefinite
programming,
Optimization Methods and Software, 11 (1999),
pp. 545581.
 K.C. Toh,
Primaldual pathfollowing algorithms for determinant
maximization problems with linear matrix
inequalities,
Computational Optimization and Applications,
14 (1999), pp. 309330.
19941998
 T.A. Driscoll, K.C. Toh and L.N. Trefethen,
From potential theory to matrix iterations in
six steps,
SIAM Review, 40 (1998), pp. 547578.
 M.J. Todd, K.C. Toh, and R.H. Tutuncu,
On the NesterovTodd direction in semidefinite
programming,
SIAM J. of Optimization, 8 (1998), pp. 769796.
 K.C. Toh and L.N. Trefethen,
The Chebyshev Polynomials of a Matrix,
SIAM J. Matrix Analysis and Applications, 20 (1998),
pp. 400419.

K.C. Toh,
GMRES vs. ideal GMRES,
SIAM J. of Matrix Analysis and Applications,
18 (1997), pp. 3036.

K.C. Toh and L.N. Trefethen,
Calculation of pseudospectra by the
Arnoldi iteration,
SIAM J. of Scientific Computing, 17 (1996), pp. 115.

K.C. Toh and L.N. Trefethen,
Pseudozeros of polynomials and pseudospectra of
companion matrices,
Numerische Mathematik, 68 (1994), pp. 403425.

K.C. Toh and S. Mukherjee,
Hypersingular and finite part integrals in the
boundary element method,
International J. of Solids and Structures, 31 (1994),
pp. 22992312.
Refereed Conference Papers

Y.C. Yuan, D.F. Sun, and K.C. Toh,
An efficient semismooth Newton based algorithm for convex clustering,
Oral presentation,
International Conference on Machine Learning (ICML) 2018.
arXiv:1802.07091.

Z.W. Li, S.G. Yang, L.F. Cheong, and K.C. Toh,
Simultaneous Clustering and Model Selection for Tensor Affinities,
Spotlight presentation,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.
 Z.Z. Zhang, G.L. Li, K.C. Toh, and W. Sung,
Inference of spatial
organizations of chromosomes using semidefinite embedding approach and HiC
data,
RECOMB 2013, The 17th Annual International Conference on Research in
Computational Molecular Biology, Beijing, China, April 710, 2013.
In "Research in Computational Molecular Biology", Lecture Notes in Computer
Science, Volume 7821, 2013, Springer, pp. 317332.
 Krishna B. Chaudhary, K.K. Phoon, and K.C. Toh,
Fast iterative solution of
large soilstructure interaction problems in varied
ground conditions,
Proceedings of 14th Asian Regional Conference on Soil Mechanics and
Geotechnical Engineering, Hong Kong, China, 2327 May 2011.
 K. B. Chaudhary, K.K. Phoon, and K.C. Toh,
Comparison of MSSOR versus ILU(0) Preconditioners for Biot's
FEM Consolidation Equations,
The 12th International Conference of
International Association for Computer Methods and Advances
in Geomechanics (IACMAG), 16 October 2008,
Goa, India.
 X. Chen, K.K. Phoon, and K.C. Toh,
Symmetric indefinite preconditioners for FE solution of
Biot's consolidation problem,
Geotechnical Engineering in the Information Technology Age
(2006): CDROM. Reston: ASCE. (GeoCongress2006, 26 Feb  1 Mar 2006, Atlanta, United
States).
 K.C. Toh, R.H. Tutuncu, and M.J. Todd,
On the implementation of SDPT3 (version 3.1)  a Matlab
software package for semidefinitequadraticlinear
programming,
IEEE Conference on ComputerAided Control System Design, Taipei, Taiwan, 24 September 2004.
 F. Ting, W.J. Heng, and K.C. Toh,
Question classification for elearning by artificial
neural network,
Fourth International Conference on Information,
Communications & Signal Processing and
Fourth IEEE PacificRim Conference On Multimedia,
1518 December 2003, Singapore.
 K.K. Phoon, K.C. Toh, S.H. Chan, and F.H. Lee,
A generalized Jacobi preconditioner for finite element
solution of largescale consolidation problems,
in Second
MIT Conference on Computational Fluid and Solid Mechanics,
1720 June 2003, Massachusetts Institute of Technology,
Cambridge, United States, Vol.1, pp. 573577, 2003.
 G.L. Zhou, K.C. Toh, and J. Sun,
Efficient algorithms for the smallest enclosing ball problem
in high dimensional space,
Novel Approaches to Hard Discrete Optimization,
Proceedings of Fields Institute of
Mathematics, P. Pardalos and H. Wolkowicz eds.,
Canadian Mathematical Society, 2002.
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Toh Kim Chuan