Professor Goldfarb's Papers

  1. "Conjugate gradient method for nonlinear programming problems with linear constraints," (with L. Lapidus), I. and E.C. Fundamentals, 7, (1968), 142-151.
  2. "Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints," SIAM J. Applied Math., 17, (1969), 739-763.
  3. "Sufficient conditions for the convergence of a variable metric algorithm," Optimization, ed. R. Fletcher, Academic Press, London (1969), 273-281.
  4. "A family of variable metric methods derived by variational means," Math. of Comp., 24, (1970), 23-26.
  5. "Extension of Newton's method and simplex methods for solving quadratic programs," Numerical Methods for Nonlinear Optimization, ed. F. Lootsma, Academic Press, London (1972), 239-254.
  6. "Modification methods for inverting matrices and solving systems of linear algebraic equations," Math. of Comp., 26, (1972), 829-852.
  7. "Variable metric and conjugate direction methods in unconstrained optimization: Recent developments," Proceedings ACM (1972), 496-506.
  8. "Matrix factorizations in optimization of nonlinear functions subject to linear constraints," Math. Programming, 10 (1976), 1-31.
  9. "Using the steepest-edge simplex algorithm to solve sparse linear programs," Sparse Matrix Computations, eds. J. Bunch and D. Rose, Academic Press (1976), 227-240.
  10. "Factorized variable metric methods for unconstrained optimization," Math. of Comp., 30, (1976), 796-811.
  11. "A practicable steepest-edge simplex algorithm," (with J.K. Reid), Math Programming, 12 (1977), 361-373.
  12. "Matrix factorization in optimization of nonlinear functions subject to linear constraint - An addendum," Math. Programming, 12 (1977), 279-280.
  13. "Generating conjugate directions without line searches using factorized variable metric updating formulas," Math. Programming, 13, (1977), 94-110.
  14. "On the Bartels-Golub decomposition for linear programming bases," Math. Programming, 13 (1977), 272-279.
  15. "Large-scale linear programming," Large-Scale Optimization, ed. P.T. Boggs, U.S. Army Research Office, Research Triangle Park, North Carolina (1978), 61-76.
  16. "Worst-case examples of steepest-edge paths on polyhedra combinatorially equivalent to hypercubes," (with W.Y. Sit) Discrete Applied Math., 1 (1979), 277-285.
  17. "Curvilinear path steplength algorithms for minimization which use directions of negative curvature," Math. Programming, 18 (1980), 31-40.
  18. "Modification and implementation of the ellipsoid algorithm for linear programming," (with M.J. Todd), Math. Programming, 23 (1980), 1-19.
  19. "The ellipsoid method: A survey," (with R.G. Bland and M.J. Todd), Operations Research, 29,(1981), 1039-1091.
  20. "Dual and primal-dual methods for solving strictly convex quadratic programs," (with A. Idnani), Numerical Analysis: Proceedings, Cocoyoc, Mexico 1981, ed. J.P. Hennart, Lecture Notes in Mathematics, No. 909, Springer-Verlag, Berlin (1982), 226-239.
  21. "Numerically stable approaches to linearly constrained optimization," Nonlinear Optimization, 1981, ed. M.J.D. Powell, Academic Press, London (1982), 141-146.
  22. "A numerically stable dual method for solving strictly convex quadratic programs," (with A. Idnani), Math. Programming, 27 (1983), 1-33.
  23. "Optimal estimation of Jacobian and Hessian matrices that arise in finite difference calculation," (with Ph. L. Toint), Math. of Comp., 43, (1984), 69-88.
  24. "Efficient dual simplex algorithms for the assignment problem," Math. Programming, 33 (1985), 187-203.
  25. "Efficient primal algorithms for strictly convex quadratic programs," Fourth IIMAS Workshop in Numerical Analysis, Guanajuato, Mexico, 1984. J.P. Hennart (ed.), Lecture Notes in Mathematics, Springer-Verlag, Berlin (1986).
  26. "Strategies for constraint deletion in active set algorithms," Numerical Analysis, eds. D.F. Griffiths and G.A. Watson, Pitman Research Notes in Mathematics Series, No. 140, Longman Scientific and Technical, Essex (1986), 66-81.
  27. "A computational comparison of the Dinic and network simplex methods for maximum flow," (with M.D. Grigoriadis) Annals of Operations Research, 13 (1988), 88-123.
  28. "A relaxed version of Karmarkar?s method," Mathematical Programming, (with S. Mehrotra), 40 (1988), 289-315.
  29. "Relaxed variants of Karmarkar?s algorithm for linear programs with unknown optimal objective value," (with S. Mehrotra), Mathematical Programming, 40 (1988), 183-195.
  30. "A self-correcting version of Karmarkar?s algorithm," (with S. Mehrotra), SIAM Journal on Numerical Analysis, 26 (1989), 1006-1015.
  31. "Linear Programming," (with M.J. Todd), Chapter II in Handbook in Operations Research and Management Science, Vol. 1, Optimization, G.L. Nemhauser, A.H.G. Rinnooy-Kan, and M.J. Todd (eds.), Elvsevier Science Publishers, B.V. (North-Holland), 1989, 73-170.
  32. "Anti-stalling pivot rules for the network simplex algorithm," (with J. Hao and S.R. Kai), Networks, 20 (1990), 79-91.
  33. "Efficient shortest path simplex algorithms," (with J. Hao and S.R. Kai), Operations Research, 38 (1990), 624-628.
  34. "A primal simplex algorithm that solves the maximum flow problem in at most nm pivots and O(n2m) time," (with J. Hao), Mathematical Programming, 47 (1990), 353-365.
  35. "Shortest path algorithms using dynamic breadth-first search," (with J. Hao and S. R. Kai), Networks, 21 (1991), 29-50.
  36. "A logarithmic barrier function algorithm for quadratically constrained convex quadratic programming," (with S. Liu and S. Wang) SIAM J. on Optimization, 1 (1991), 252-267.
  37. "An O(n3L) primal interior point algorithm for convex quadratic programming," (with S. Liu) Mathematical Programming, 49 (1991), 325-340.
  38. "Solving multicommodity network flow problems by an interior point method," (with I.C. Choi), Large-Scale Numerical Optimization, T. Coleman and Q. Li eds., SIAM, Philadelphia (1990), 58-69.
  39. "On strongly polynomial variants of the network simplex algorithm for the maximum flow problem," (with J. Hao), Operations Research Letters, 10 (1991), 383-387.
  40. "A primal projective interior point method for linear programming," with (D. Xiao), Mathematical Programming, 51 (1991), 17-43.
  41. "Polynomial-time primal simplex algorithms for the minimum cost network flow problem," (with J. Hao) Algorithmica, 8 (1992), 145-160.
  42. "Steepest edge simplex algorithms for linear programming" (with J. J. Forrest), Mathematical Programming, 57 (1992), pp. 341-374.
  43. "Partial-update Newton methods for unary, factorable, and partially separable optimization," (with S. Wang), SIAM J. on Optimization, 3 (1993), 382-397.
  44. "An O(n3L) primal-dual potential reduction algorithm for solving convex quadratic programs" (with S. Liu), Mathematical Programming, 61 (1993), 161-170.
  45. "Exploiting special structure in a primal-dual path-following algorithm," (with I. C. Choi), Mathematical Programming, 58 (1993), 33-52.
  46. "On the maximum capacity augmenting path algorithm for the maximum flow problem," (with J. Hao), Discrete Applied Mathematics, 47 (1993), 9-16.
  47. "A path-following projective interior point method for linear programming," (with D. X. Shaw), SIAM J. on Optimization, 4 (1994), 65-85.
  48. "On solution containing ellipsoids in linear programming" (with I.C. Choi), Journal of Optimization Theory and Applications, 80 (1994), 165-177.
  49. "On the complexity of the simplex method" Advances in Optimization and Numerical Analysis, S. Gomez and J-P Hennart, eds., Kluwer Academic Publishers, 1994, 25-38.
  50. "Algorithms for unconstrained optimization: a review of recent developments" in Mathematics of Computation 1943-1993, W. Gautschi, ed., Proceedings of Symposia in Applied Mathematics, Amer. Math. Soc. 1994, 33-48.
  51. "On the complexity of a class of projective interior point methods," (with D. Shaw), Mathematics of Operations Research, 20 (1995), 116-134.
  52. "Data-parallel implementations of dense simplex methods on the Connection Machine CM-2" (with J. Eckstein, I.I. Boduroglu, and L. Polymenakos) ORSA Journal on Computing, 7 (1995), 402-416.
  53. "A faster combinatorial algorithm for the generalized circulation problem" (with Z. Jin) Mathematics of Operations Research, 21 (1996), 529-539.
  54. "On strongly polynomial dual simplex algorithms for the maximum flow problem" (with W. Chen) MathematicalProgramming, 78 (1997), 159-168.
  55. "A polynomial-time highest-gain augmenting path algorithm for the generalized circulation problem" (with J. Orlin and Z. Jin) Mathematics of Operations Research, 22 (1997), 793-802.
  56. "Strongly polynomial dual simplex methods for the maximum flow problem" (with R. Armstrong, W. Chen and Z. Jin) Mathematical Programming, 80 (1998) 17-33.
  57. "Interior point trajectories in semidefinite programming" (with K. Scheinberg) SIAM J. on Optimization, 8(1998) 871-866.
  58. "An O(nm)-time network simplex algorithm for the shortest path problem" (with Z. Jin) Operations Research, 47 (1999) 445-448.
  59. "A new scaling algorithm for the minimum cost network flow problem" (with Z. Jin)  Operations Research Letters, 25 (1999) 205-211.
  60. "On parametric semidefinite programming" (with K. Scheinberg) Applied Numerical Methods, 29 (1999) 361-377.
  61. "A modified barrier-augmented Lagrangean method for constrained minimization" (with K. Scheinberg, R. Polyak and B. Yusefovich) Computational Optimization and Applications,14 (1999) 55-74.
  62. "A polynomial dual simplex algorithm for the generalized circulation problem" (with Z. Jin and Y. Lin)  Mathematical Programming, 91 (2002) 271-288.
  63. "Combinatorial interior point methods for generalized network flow problems" (with Y. Lin) Mathematical Programming ,93 (2002) 227-246.
  64. "Second-order cone programming" (with F. Alizadeh) Mathematical Programming, 95 (2003) 3-51.
  65. "Robust portfolio selection problems" (with G. Iyengar) Mathematics of Operations Research, 28 (2003) 1-38.
  66. "Robust quadratically constrained quadratic programs" (with G. Iyengar) Mathematical Programming, 97 (2003) 495-515.
  67. "A product-form Cholesky factorization method for handling dense columns in interior point methods for linear programming" (with K. Scheinberg) Mathematical Programming, 99 (2004) 1-34.
  68. "Product-form Cholesky factorization in interior point methods for second-order cone programming" (with K. Scheinberg) to appear in Mathematical Programming,103 (2005) 135-179.
  69. "An iterative regularization for method total variation based image restoration" (with S. Osher, M. Burger, J. Xu and W. Yin) SIAM J. on Multiscale Model. Simul., 4 (2005), 460-489.
  70. "Second-order cone programming based methods for total variation image restoration" (with W. Yin) SIAM J. on Scientific Computing, 27 (2005), 622-645.
  71. "Image cartoon-texture decomposition and features selection using the total variation regularized L1 functional" (with S. Osher and W. Yin) Lecture Notes in Computer Science, 3752 (2005), 73-84.
  72. "Interior-point l2 - penalty methods for noncovex nonlinear programming with strong global convergence properties" (with L. Chen) Mathematical Programming, 108 (2006), 1-36.
  73. "The total variation regularized L1 model for multi-scale decomposition", (with W. Yin and S. Osher) SIAM J. on Mulitscale Model. Simul., 6 (2007), 190-211.
  74. "A comparison of three total variation-based texture extraction models", (with W. Yin and S. Osher) Journal of Visual Communication and Image Representation, (2007) to appear.
  75. "Bregman iterative algorithms for l1 minimization with applications to compressed sensing ", (with W. Yin, S. Osher and J. Darbon) SIAM J. on Imaging Sciences, 1 (2008).
  76. "Robust active portfolio management", (with E. Erdogan and G. Iyengar) Journal of Computational Finance 11 Number 4 (2008) 71-98.
  77. "Numerically stable LDLT interior point methods for convex quadratic programming", (with K. Scheinberg) IMA Journal of Numerical Analysis. 28 (2008) 806-826.
  78. "A curvilinear search method for p-harmonic flows on spheres", (with Z. Wen and W. Yin) SIAM J. on Imaging Sciences 2 (2009) 84-109.
  79. "A line search multigrid method ofr large-scale convex optimization", (with Z. Wen) SIAM J. on Optimization 20 (2009) 1478-1503.
  80. "Fast minimization of total variation based energies via parametric maximum flows", (with W. Yin) SIAM J. Scientific Computing 31 (2009) 3712-3743.
  81. "An interior-point piecewise linear penalty method for nonlinear programming", (with L. Chen) submitted to Mathematical Programming to appear (published online: 14 July 2009).
  82. "Fixed point and Bregman iterative methods for matrix rank minimization", (with S. Ma amd L. Chen) submitted to Mathematical Programming to appear (published online: 23 September 2009).
  83. "Approximation Algorithms for the Multi-Item Lot-Sizing Problem with Batch Capacities", (with L. Chen) submitted to Operations Research.
  84. "An active set method for mathematical programs with linear complementarity constraints", (with L. Chen) submitted to SIAM J. on Optimization.
  85. "A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation", (with Z. Wen, W. Yin and Y. Zhang) submitted to SIAM J. on Scientific Computing.
  86. "A row-by-row method for semidefinite programming", (with Z. Wen, S. Ma and K. Scheinberg) submitted to SIAM J. on Optimization.
  87. "Convergence of fixed point continuation algotithms for matrix rank minimization", (with S. Ma) submitted to Foundations of Computational Mathematics.
  88. "Alternating Direction Augmented Lagrangian Methods for Semidefinite Programming", (with Z. Wen and W. Yin) submitted to Mathematical Programming Computation.
  89. "Local Search Approximation Algorithms for the One-Warehouse Multi-Retailer Problem", (with L. Chen) in preparation.
  90. "Fast Alternating Linearization Methods for Minimizing the Sum of Two Convex Functions", (with S. Ma) submitted to SIAM J. on Optimization.
  91. "Fast Multiple Splitting Algorithms for Convex Optimization", (with S. Ma) submitted to SIAM J. on Optimization.

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