SBmethod - A C++ Implementation of the Spectral Bundle Method. (no longer supported, please use the ConicBundle callable library instead) SBmethod implements the spectral bundle method of Helmberg and Rendl [2000]; Helmberg and Kiwiel [1999] for minimizing the maximum eigenvalue of an affine matrix function (real and symmetric). The code is intended for large scale problems. It supports sign constraints on the design variables and allows to exploit structural properties of the matrices such as sparsity and low rank structure. The code comes with ABSOLUTELY NO WARRANTY and is free under the terms of the Gnu General Public License, Version 2.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Billionnet, Alain; Elloumi, Sourour; Lambert, Amélie; Wiegele, Angelika: Using a conic bundle method to accelerate both phases of a quadratic convex reformulation (2017)
  2. Malick, Jérôme; Roupin, Frédéric: On the bridge between combinatorial optimization and nonlinear optimization: a family of semidefinite bounds for 0--1 quadratic problems leading to quasi-Newton methods (2013)
  3. Malick, Jérôme; Roupin, Frédéric: Solving (k)-cluster problems to optimality with semidefinite programming (2012)
  4. Sivaramakrishnan, Kartik Krishnan; Mitchell, John E.: Properties of a cutting plane method for semidefinite programming (2012)
  5. Billionnet, Alain; Elloumi, Sourour; Plateau, Marie-Christine: Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method (2009)
  6. Jansson, Christian: On verified numerical computations in convex programming (2009)
  7. Nayakkankuppam, Madhu V.: Solving large-scale semidefinite programs in parallel (2007)
  8. Braun, Stephen; Mitchell, John E.: A semidefinite programming heuristic for quadratic programming problems with complementarity constraints (2005)
  9. Helmberg, C.: Numerical evaluation of SBmethod (2003)
  10. Krishnan, Kartik; Mitchell, John E.: Semi-infinite linear programming approaches to semidefinite programming problems (2003)
  11. Parrilo, Pablo A.; Lall, Sanjay: Semidefinite programming relaxations and algebraic optimization in control (2003)
  12. Anjos, Miguel F.; Wolkowicz, Henry: Strengthened semidefinite relaxations via a second lifting for the Max-Cut problem (2002)