Preprints

  1. J.F. Yang, D.F. Sun, and K.C. Toh, A proximal point algorithm for log-determinant optimization with group Lasso regularization, preprint, National University of Singapore, 2012.
  2. K.F. Jiang, D.F. Sun, and K.C. Toh, A partial proximal point algorithm for nuclear norm regularized matrix least squares problems,, preprint, National University of Singapore, Feb 2012.
  3. K.F. Jiang, D.F. Sun, and K.C. Toh, An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP, preprint, National University of Singapore, Sep 2011.
  4. B. Wu, C. Ding, D.F. Sun, and K.C. Toh, On the Moreau-Yoshida regularization of the vector k-norm related functions, preprint, National University of Singapore, March 2011.
  5. C. Ding, D.F Sun and K.C. Toh, An introduction to a class of matrix cone programming, preprint, National University of Singapore, Sep 2010.

Book chapters

  1. K.C. Toh, M.J. Todd, and R.H. Tutuncu, On the implementation and usage of SDPT3 -- a Matlab software package for semidefinite-quadratic-linear 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, 2011.
    Here is the complete performance results obtained by SDPT3-4.0 on over 400 problems.
  2. X.Y. Fang and K.C. Toh, Using a distributed SDP approach to solve simulated protein molecular conformation problems, in Handbook on Distance Geometry with applications to molecular conformation and sensor networks, A. Mucherino, C. Lavor L. Liberti and N. Maculan eds., Springer, to appear.

Accepted and published journal papers

  1. X.Y. Zhao, and K.C. Toh, Infeasible potential reduction algorithms for semidefinite programming, Pacific J. Optimization, accepted, Apr 2012.
  2. 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. Geomechancis, accepted, Dec 2011.
  3. K. B. Chaudhary, K.K. Phoon, and K.C. Toh, Effective block diagonal preconditioners for Biot's consolidation equations in piled-raft foundations, International J. Numerical and Analytical Methods in Geomechanics, accepted, Nov 2011.
  4. X. Chen, K.K. Phoon, and K.C. Toh, Performance of zero-level fill-in preconditioning techniques for iterative solutions in geotechnical applications, International J. Geomechanics, accepted, Mar 2011.
  5. 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. 573--596.
  6. 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. 399--436. Matlab software PPApack
  7. 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. 331--355.
  8. L. Li, and K.C. Toh, A polynomial-time inexact primal-dual infeasible path-following algorithm for convex quadratic SDP, Pacific J. Optimization, 7 (2011), pp. 43--61.
  9. S. Yun, and K.-C. Toh, A coordinate gradient descent method for L1-regularized convex minimization, Computational Optimization and Applications, 48 (2011), pp. 273--307.

    2006--2010

  10. 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. 615--640. Matlab software NNLS
    Numerical results suggest that our algorithm is efficient and robust in solving large-scale 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.
  11. Lu Li and K.C. Toh An inexact interior point method for L1-regularized sparse covariance selection, Mathematical Programming Computation, 2 (2010), pp. 291--315.
  12. L. Li, and K.C. Toh, A polynomial-time inexact interior-point method for convex quadratic symmetric cone programming, J. Math-for-industry, 2 (2010), pp. 199--212.
  13. C.J. Wang, D.F. Sun, and K.C. Toh, Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm, SIAM J. Optimization, 20 (2010), pp. 2994--3013. Matlab software LogdetPPA
  14. X.Y. Zhao, D.F. Sun, and K.C. Toh, A Newton-CG augmented Lagrangian method for semidefinite programming, SIAM J. Optimization, 20 (2010), pp. 1737--1765. 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 1e-6.
  15. X.-W. Liu, G.Y. Zhao, and K.C. Toh, On the implementation of a log-barrier progressive hedging method for multistage stochastic programs, J. of Computational and Applied Mathematics, 234 (2010), pp. 579--592.
  16. N.-H. Z. Leung and K.-C. Toh, An SDP-based divide-and-conquer algorithm for large scale noisy anchor-free graph realization, SIAM J. Scientific Computing, 31 (2009), pp. 4351--4372.
    A movie showing how the divide-and-conquer algorithm computes the conformation of a protein molecule.
    Matlab software DISCO
  17. P. Biswas, K.C. Toh, and Y. Ye, A distributed SDP approach for large scale noisy anchor-free graph realization with applications to molecular conformation, SIAM J. Scientific Computing, 30 (2008), pp. 1251--1277.
  18. K.C. Toh, An inexact primal-dual path-following algorithm for convex quadratic SDP, Mathematical Programming, 112 (2008), pp. 221--254.
  19. K.C. Toh, and K.K. Phoon, Comparison between iterative solution of symmetric and non-symmetric forms of Biot’s FEM equations using the generalized Jacobi preconditioner, International Journal for Numerical and Analytical Methods in Geomechanics, 32 (2007), pp. 1131--1146.
  20. X. Chen, K.K. Phoon, and K.C. Toh, Partitioned versus global Krylov subspace iterative methods for FE solution of 3-D Biot's problem, Computer Methods in Applied Mechanics and Engineering, 196 (2007), pp. 2737--2750.
  21. 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. 221--247.
  22. K.C. Toh, R.H. Tutuncu, and M.J. Todd, Inexact primal-dual path-following 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. 135--164.
  23. R.M. Freund, F. Ordonez, and K.C. Toh, Behavioral measures and their correlation with IPM iteration counts on semi-definite programming problems, Mathematical Programming, 109 (2007), pp. 445--475.
  24. Z. Cai and K.C. Toh, Solving second order cone programming via the augmented systems, SIAM J. Optimization, 17 (2006), pp. 711--737.
  25. 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. 360--371.
    Matlab codes for solving small size sensor network localization problems.
  26. 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. 785--807.
  27. 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. 419--443.

    2001--2005

  28. G.L. Zhou, and K.C. Toh, Superlinear convergence of a Newton-type algorithm for monotone equations, J. Optimization Theory and Applications, 125 (2005), pp. 205--221.
  29. G.L. Zhou, K.C. Toh, and J. Sun, Efficient algorithms for the smallest enclosing ball problem, Computational Optimization and Applications, 30 (2005), pp. 147--160.
  30. K.K. Phoon, K.C. Toh, and X. Chen, Block constrained versus generalized Jacobi preconditioners iterative solution of large-scale Biot's FEM equations, Computers and Structures, 82 (2004), pp. 2401--2411.
  31. 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. 291--318.
  32. 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. 1361--1381.
  33. K. C. Toh, Solving large scale semidefinite programs via an iterative solver on the augmented systems, SIAM J. Optimization, 14 (2004), pp. 670--698.
  34. 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. 269--283.
  35. G.L. Zhou, and K.C. Toh, Polynomiality of An Inexact Infeasible Interior Point Algorithm for Semidefinite Programming, Mathematical Programming, 99 (2004), pp. 261--282.
  36. Phoon, K. K., Toh, K. C., Chan, S. H., and Lee, F. H., Fast iterative solution of large undrained soil-structure interaction problems, International Journal for Numerical and Analytical Methods in Geomechanics, 27 (2003), pp. 159--181.
  37. 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. 357--377.
  38. R.H Tutuncu, K.C. Toh, and M.J. Todd, Solving semidefinite-quadratic-linear programs using SDPT3, Mathematical Programming Ser. B, 95 (2003), pp. 189--217.
  39. 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. 377--400.
  40. K.C. Toh, G.Y Zhao, and J. Sun, A multiple-cut analytic center cutting plane method for semidefinite feasibility problems, SIAM J. Optimizaton, 12 (2002), pp. 1126--1146.
  41. 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. 332--346.
  42. K.C. Toh, and M. Kojima, Solving some large scale semidefinite programs via the conjugate residual method, SIAM J. Optimization, 12 (2002), pp. 669--691.
  43. K.C. Toh, A note on the calculation of step-lengths in interior-point methods for semidefinite programming, Computational Optimization and Applications, 21 (2002), pp. 301--310.
  44. 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. 57--76.

    1994--2000

  45. K.C. Toh, Some new search directions for primal-dual interior point methods in semidefinite programming, SIAM J. Optimization, 11 (2000), pp. 223--242.
  46. 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. 145--165.
  47. 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. 545--581.
  48. K.C. Toh, Primal-dual path-following algorithms for determinant maximization problems with linear matrix inequalities, Computational Optimization and Applications, 14 (1999), pp. 309--330.
  49. T.A. Driscoll, K.C. Toh and L.N. Trefethen, From potential theory to matrix iterations in six steps, SIAM Review, 40 (1998), pp. 547-578.
  50. M.J. Todd, K.C. Toh, and R.H. Tutuncu, On the Nesterov-Todd direction in semidefinite programming, SIAM J. of Optimization, 8 (1998), pp. 769--796.
  51. K.C. Toh and L.N. Trefethen, The Chebyshev Polynomials of a Matrix, SIAM J. Matrix Analysis and Applications, 20 (1998), pp. 400-419.
  52. K.C. Toh, GMRES vs. ideal GMRES, SIAM J. of Matrix Analysis and Applications, 18 (1997), pp. 30--36.
  53. K.C. Toh and L.N. Trefethen, Calculation of pseudospectra by the Arnoldi iteration, SIAM J. of Scientific Computing, 17 (1996), pp. 1--15.
  54. K.C. Toh and L.N. Trefethen, Pseudozeros of polynomials and pseudospectra of companion matrices, Numerische Mathematik, 68 (1994), pp. 403--425.
  55. 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. 2299--2312.

Conference papers

  1. 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), 1-6 October 2008, Goa, India.
  2. 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).
  3. K.C. Toh, R.H. Tutuncu, and M.J. Todd, On the implementation of SDPT3 (version 3.1) -- a Matlab software package for semidefinite-quadratic-linear programming, IEEE Conference on Computer-Aided Control System Design, September 2004, Invited Paper.
  4. F. Ting, W.J. Heng, and K.C. Toh, Question classification for e-learning by artificial neural network, Fourth International Conference on Information, Communications & Signal Processing and Fourth IEEE Pacific-Rim Conference On Multimedia, 15-18 December 2003, Singapore.
  5. K.K. Phoon, K.C. Toh, S.H. Chan, and F.H. Lee, A generalized Jacobi preconditioner for finite element solution of large-scale consolidation problems, in Second MIT Conference on Computational Fluid and Solid Mechanics, 17--20 June 2003. Massachusetts Institute of Technology, Cambridge, United States.
  6. 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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