Other Algorithmic Approaches

• C. Helmberg, M. L. Overton and F. Rendl.
  "The Spectral Bundle Method with Second-Order Information",
  Preprint 2012-10, Fakultät für Mathematik, TU Chemnitz, September 2012.
  opt-online
• M. Kilic, E. Mengi, and E. A. Yildirim.
  "Numerical Optimization of Eigenvalues of Hermitian Matrix Functions",
  Technical Report, Department of Mathematics, Koc University, Sariyer, 34450, Istanbul, Turkey, February 2012.
  opt-online
• M. Baes, M. Bürgisser, and A. Nemirovski.
  "A randomized Mirror-Prox method for solving structured large-scale matrix saddle-point problems",
  .Technical report, ETH Zurich / Georgia Institute of Technology, December 2011.
  opt-online
• Y. Nesterov and V. Protasov.
  "Optimizing the Spectral Radius",
  Center for Operations Research and Econometrics (CORE), Universite catholique de Louvain (UCL), December 2011.
  opt-online
• 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, September 2011 .
  opt-online
• Renato D. C. Monteiro, Camilo Ortiz and Benar B. F. Svaiter.
  "Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems",
  School of Industrial and Systems Engineering, Georgia Institute of Technology, May 2011.
  opt-online
• T. Davi and F. Jarre.
  "Solving large scale problems over the doubly nonnegative cone",
  Preprint, Universität Düsseldorf, April 2011.
  opt-online
• T. Davi and F. Jarre.
  "High accuracy solution of large scale semidefinite programs",
  Preprint, Universität Düsseldorf, April 2011.
  To appear in Optimizaton Methods and Software.
  opt-online
• D. Henrion and J. Malick.
  "Projection methods in conic optimization",
  To appear as a contributed chapter of "Handbook of Semidefinite, Cone and Polynomial Optimization" edited by M. Anjos and J. B. Lasserre, Springer, 2011.
  opt-online
• K. C. Kiwiel.
  "Inexact Dynamic Bundle Methods",
  Tech. report, Systems Research Institute, Warsaw, December 2010.
  opt-online
• Xuan Vinh Doan, Serge Kruk and H. Wolkowicz.
  "A Robust Algorithm for Semidefinite Programming",
  CORR 2010-09, Department of Combinatorics and Optimization, University of Waterloo, Novemberg 2010.
  opt-online
• Z. Wen and W. Yin.
  "A Feasible method for Optimization with Orthogonality Constraints",
  Rice University, November 2010.
  opt-online
• L. Huiling.
  "The Inexact Spectral Bundle Method for Convex Quadratic Semidefinite Programming",
  School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore, November 2010.
  opt-online
• L. Grippo, L. Palagi, M. Piacentini, V. Piccialli, and G. Rinaldi.
  "SpeeDP: A new algorithm to compute the SDP relaxations of Max-Cut for very large graphs",
  Technical Report DII-UTOVRM 13.10 Dipartimento di Ingegneria dell'Impresa University of Rome Tor Vergata, September 2010.
  opt-online
• G. Iyengar, D. Phillips, and C. Stein.
  "Feasible and accurate algorithms for covering semidefinite programs",
  Proceedings of the 12th Scandinavian Workshop on Algorithms and Theory, pp. 150-162, 2010.
  opt-online
• M. Bürgisser and M. Baes.
  "Smoothing techniques for solving semidefinite programs with many constraints",
  IFOR Internal report, ETH Zurich, October 2009.
  opt-online
• C. Wang, D. Sun, and K.-C. Toh.
  "Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm",
  National University of Singapore, September 2009.
  opt-online
• Z. Wen, D. Goldfarb and W. Yin.
  "Alternating Direction Augmented Lagrangian Methods for semidefinite programming",
  Department of IEOR, Columbia University, August 2009.
  opt-online
• C. B. Chua, H. Lin and P. Yi.
  "Uniform nonsingularity and complementarity problems over symmetric cones",
  Research report, School of Physical and Mathematical Sciences, Nanyang Technological Unversity, Singapore, July 2009 .
  opt-online
• K. Scheinberg and I. Rish.
  "SINCO - a greedy coordinate ascent method for sparse inverse covariance selection problem",
  IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598, July 2009.
  opt-online
• C. B. Chua and P. Yi.
  "A continuation method for nonlinear complementarity problems over symmetric cone",
  Research Report, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, April 2009.
  opt-online
• Z. Wen, D. Goldfarb, S. Ma, and K. Scheinberg.
  "Row by row methods for semidefinite programming",
  Dept of IEOR, Columbia University, April 2009.
  opt-online
• F. Dabbene, P. S. Shcherbakov, and B. T. Polyak.
  "A Randomized Cutting Plane Method with Probabilistic Geometric Convergence",
  IEIIT-CNR, Politecnico di Torino, Italy, November 2008.
  opt-online
• J. Malick, J. Povh, F. Rendl and A. Wiegele.
  "Regularization methods for semidefinite programming",
  Technical Report, Alpen-Adria-Universität Klagenfurt, Austria, October 2007.
  opt-online
• R. Garcés, W. G. Bofill, F. Jarre.
  "Two theoretical results for sequential semidefinite programming",
  Preprint, Mathematisches Institut, Universität Düsseldorf, Nov. 2007.
  opt-online
• Y. Nesterov.
  "Gradient methods for minimizing composite objective function",
  CORE Discussion Paper 2007/76 September 2007.
  opt-online
• M. Stingl, M. Kocvara and G. Leugering.
  "A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization",
  Preprint 317, Institute of Applied Mathematics, University of Erlangen-Nuremberg, 2007 .
  opt-online
• K. K. Sivaramakrishnan and J. E. Mitchell.
  "Properties of a cutting plane algorithm for semidefinite programming",
  Technical Report, Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, September 2007.
  opt-online
• F. Jarre and F. Rendl.
  "An Augmented Primal-Dual Method for Linear Conic Programs",
  Report, Institut für Mathematik, Universität Düsseldorf, April 2007..
  opt-online
• G. Lan, Z. Lu, and R.D.C. Monteiro.
  "Primal-dual first-order methods with ${\cal O}(1/\epsilon)$ iteration-complexity for cone programming",
  Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205 USA, December 2006.
  opt-online
• J. E. Mitchell and V. L. Basescu.
  "Selective Gram-Schmidt orthonormalization for conic cutting surface algorithms",
  Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, November 2006.
  opt-online
• W. Gomez and H. Ramirez.
  "A Filter Algorithm for Nonlinear Semidefinite Programming",
  CMM-B-06/10 - 171 Centre for Mathematical Modelling, UMR 2071, Universidad de Chile-CNRS. Casilla 170-3 Santiago 3, Chile October 2006.
  opt-online
• A. Belloni, R. M. Freund, and S. Vempala.
  "An Efficient Re-scaled Perceptron Algorithm for Conic Systems",
  Technical Report RC24073, October/2006 IBM T.J. Watson Research Center 1101 Kitchawan Road, Yorktown Heights, NY 10598.
  opt-online
• O. P. Ferreira, P. R. Oliveira, R. C. M. Silva.
  "On the Convergence of the Entropy-Exponential Penalty Trajectories and Generalized Proximal Point Methods in Semidefinite Optimization",
  Universidade Federal do Rio de Janeiro, July 2006.
  opt-online
• V. L. Basescu and J. E. Mitchell.
  "An analytic center cutting plane approach for conic programming",
  Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 USA, June 2005.
  opt-online
• C. Jansson.
  "Termination and Verification for Ill-Posed Semidefinite Programming Problems",
  Informatik III, TU Hamburg-Harburg, Schwarzenbergstr. 95, 21073 Hamburg, June 2005.
  opt-online
• M. V. Nayakkankuppam.
  "Solving Large-Scale Semidefinite Programs in Parallel",
  Technical Report, Department of Mathematics & Statistics, University of Maryland, Baltimore County, March 2005.
  opt-online
• M. Kocvara and M. Stingl.
  " On the solution of large-scale SDP problems by the modified barrier method using iterative solvers",
  Research Report 304, Institute of Applied Mathematics, University of Erlangen, March 2005.
  opt-online
• Z. Lu, A. Nemirovski and R.D.C. Monteiro.
  "Large-Scale Semidefinite Programming via Saddle Point Mirror-Prox Algorithm",
  Technical report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA, November, 2004.
  opt-online
• Yu. Nesterov.
  "Smoothing technique and its applications in Semidefinite Optimization",
  Mathematical Programming 110, No. 2 (A), 245-259 (2007).
  CORE Discussion Paper, Springer Link
• S. Burer and C. Choi.
  "Computational Enhancements in Low-Rank Semidefinite Programming",
  Manuscript, Department of Mangagement Sciences, University of Iowa, July 2004.
  opt-online
• M. R. Oskoorouchi and J.-L. Goffin.
  "A matrix generation approach for eigenvalue optimization",
  College of Business Administration, California State University San Marcos, San Marcos, California, USA 92096-0001, April 2004.
  opt-online
• Katsuki Fujisawa , Mituhiro Fukuda , Kazuhide Nakata.
  "Preprocessing sparse semidefinite programs via matrix completion",
  IMA Preprint Series \# 1969, Institute for Mathematics and its Applications, University of Minnesota, 514 Vincent Hall, 206 Church Street S. E., Minneapolis, MN 55455-0436 USA, March 2004. Revised July 2004.
  Also issued as Research Report B-401, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-okayama Meguro, Tokyo, 152-8552, Japan.
  opt-online
• S. Burer and R.D.C. Monteiro.
  "Local Minima and Convergence in Low-Rank Semidefinite Programming",
  Technical report, Department of Management Sciences, University of Iowa, September 2003.
  opt-online
• J. E. Mitchell and K. Krishnan.
  "Properties of a Cutting Plane Method for Semidefinite Programming",
  Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 USA, May 2003.
  opt-online
• C. B. Chua.
  "A primal-dual second order cone approximations algorithm for symmetric cone programming",
  School of Operations Research and Industrial Enginneering, Cornell University, March 2003. .
  opt-online
• J. Sun, D. Sun, and L. Qi.
  "Quadratic Convergence of a Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems",
  Technical Report, Department of Decision Sciences, National University of Singapore, Republic of Singapore 119260, 2000, revised April 2002.
  pdf-file (http)
• C. Kanzow and C. Nagel.
  "Semidefinite Programs: New Search Directions, Smoothing-Type Methods, and Numerical Results",
  SIAM Journal on Optimization Volume 13, Number 1, pp. 1-23, May 2002.
  SIAM Journals Online
• M. van Bossum.
  "Semidefinite optimization, a spectral approach",
  PhD-Thesie, Faculteit der Wiskunde en Informatica, Universiteit Utrecht, May 2002.
• R. M. B. Goes and P. R. Oliveira. "A new class of merit functions for the semidefinite complementarity problem",
  ES-569, Programa de Engenharia de sistemas e Computacao/COPPE/Federal University of Rio de Janeiro, January 2002.
  optimization-online
• H. Bauschke and S. Kruk. "The method of reflection-projection for convex feasibility problems with an obtuse cone",
  Technical report, Oakland University, Rochester MI, February 2002.
  optimization-online
• D. Sun and J. Sun.
  "Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems",
  Manuscript, Department of Decision Sciences / Department of Mathematics, National University of Singapore, Singapore 119260, Aug. 2001.
  optimization-online
• S. Burer, R. D.C. Monteiro, and Yin Zhang.
  "Solving a Class of Semidefinite Programs via Nonlinear Programming",
  Combined and revised version of thechnical reports TR99-17 and TR99-23, Dept. of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, USA, 2001.
  optimization-online
• S. Burer, R.D.C. Monteiro, and Y. Zhang.
  "A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs",
  Working paper, School of ISyE, Georgia Tech, Atlanta, GA, USA, June 2001.
  ps.gz-file (http), dvi-file (http)
• K. Krishnan and J. Mitchell.
  "A Linear Programming Approach to Semidefinite Programming Problems",
  Department of Mathematical Sciences, Rensselaer Polytechnic Institute, May 2001.
  opt-online, ps-file (http), dvi-file (http)
• S. Burer and R. D. C. Monteiro.
  "A Nonlinear Programming Algorithm for Solving Semidefinite Programs via Low-rank Factorization",
  School of ISyE, Georgia Tech, Atlanta, March 2001.
  ps-file (http) or dvi-file (http)
• C. Helmberg and K.C. Kiwiel.
  "A Spectral Bundle Method with Bounds",
  Mathematical Programming 93(2) (2002) pp. 173-194.
  ps-file (ftp)
• S. Burer, R.D.C. Monteiro, and Y. Zhang.
  "Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation",
  Technical Report TR99-27, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, November 1999.
  ps-file (http)
• R.J. Vanderbei and H. Y. Benson.
  "On Formulating Semidefinite Programming Problems as Smooth Convex Nonlinear Optimization Problems",
  ORFE 99-01, Dept. of Operations Research and Financial Engineering, Princeton University, Princeton NJ, November 1999.
  ps.gz-file (http) or pdf-file (http)
• S. Burer, R.D.C. Monteiro, and Y. Zhang.
  "Solving Semidefinite Programs via Nonlinear Programming
  Part II: Interior Point Methods for a Subclass of SDPs",
  Technical Report TR99-23, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, October 1999.
  ps-file (http) or dvi-file (http)
• S. Burer, R.D.C. Monteiro, and Y. Zhang.
  "Solving Semidefinite Programs via Nonlinear Programming
  Part I: Transformations and Derivatives",
  School of Industrial and Systems Engineering,Georgia Institute of Technology, Atlanta, GA 30332, September 1999.
  ps.gz-file (http) or dvi.gz-file (http)
• L. Mosheyev and M. Zibulevsky.
  "Penalty/Barrier Multiplier Algorithm for Semidefinite Programming",
  Optimization Methods and Software, Vol. 13, No. 4, August 2000, 235-261.
  ps.gz-file (http) or dvi.gz-file (http)
• J.V. Burke, A.S. Lewis and M.L. Overton.
  "Optimizing Matrix Stability",
  NYU Computer Science Dept Technical Report 791, September 1999. Submitted to Proceedings of the AMS.
  ps.gz-file (http)
• J.V. Burke and M.L. Overton.
  "Variational Analysis of Non-Lipschitz Spectral Functions",
  NYU Computer Science Dept Technical Report 790, September 1999. Submitted to Math Programming.
  ps.gz-file (http)
• F. Oustry.
  "A Second-Order Bundle Method to Minimize the Maximum Eigenvalue Function",
  RR-3738, INRIA Rhone-Alpes, ZIRST - 655 avenue de l'Europe, F-38330 Montbonnot Saint-Martin, July 1999.
  ps.gz-file (ftp)
• C. Helmberg and F. Rendl.
  "A Spectral Bundle Method for Semidefinite Programming",
  SIAM J. Optim. Vol. 10, No. 3, pp. 673-696.
  ps.Z-file (ftp) and abstract (http)
• F. Oustry.
  "U-Lagrangian of the maximum eigenvalue function",
  Technical Report, INRIA-ENSTA, France, November 1996.
• J. B. Lasserre.
  "Linear Programming with positive semi-definite matrices",
  Mathematical Problems in Engineering 2, pp. 499-522, 1996.
• A. S. Lewis and M. L. Overton.
  "Eigenvalue Optimization",
  Acta Numerica 1996, pp. 149-190, Cambridge University Press.
• F. Rendl and H. Wolkowicz.
  "A Semidefinite Framework for Trust Region Subproblems with Applications to Large Scale Minimization",
  Mathematical Programming 77 (1997) 273-299.
  ps.gz-file (ftp)
• A. Shapiro and M. K. H. Fan.
  "On Eigenvalue Optimization",
  SIAM J. Optim., Vol. 5, No. 3, pp. 552--569, 1995.
• M. L. Overton.
  "Large-Scale Optimization of Eigenvalues",
  SIAM J. Optim., Vol. 2, No. 1, pp. 88-120, February 1992.
  dvi-file
• M. L. Overton.
  "On minimizing the maximum eigenvalue of a symmetric matrix",
  SIAM J. Matrix Anal. Appl., Vol. 9, No. 2, April 1988.
• R. Fletcher.
  "Semi-definite matrix constraints in optimization",
  SIAM J. Control and Optimization, Vol.23, No. 4, July 1985.
• J. Cullum, W. E. Donath, and P. Wolfe.
  "The minimization of certain nondifferentiable sums of eigenvalues of Symmetric Matrices",
  Mathematical Programming Study 3 (1975) 35-55.