Helmberg, C.; Rendl, F. A spectral bundle method for semidefinite programming. (English) Zbl 0960.65074 SIAM J. Optim. 10, No. 3, 673-696 (2000). Semidefinite programming problems with constant trace on the primal feasiblle set are equivalent to eigenvalue optimization problems. These are convex nonsmooth programming problems and can be solved by bundle methods. The authors propose replacing the traditional polyhedral cutting plane model constructed from subgradient information by a semidefinite model that is tailored to eigenvalue problems. Convergence follows from the traditional approach and a proof is included for completeness. Numerical examples demonstrating the efficiency of the approach on combinatorial examples are presented. Reviewer: Stefan Mititelu (Bucureşti) Cited in 5 ReviewsCited in 163 Documents MSC: 65K05 Numerical mathematical programming methods 90C22 Semidefinite programming 90C25 Convex programming 90C06 Large-scale problems in mathematical programming 52A41 Convex functions and convex programs in convex geometry Keywords:eigenvalue optimization; convex optimization; semidefinite programming; proximal bundle method; large-scale problems; convergence; numerical examples Software:COL PDFBibTeX XMLCite \textit{C. Helmberg} and \textit{F. Rendl}, SIAM J. Optim. 10, No. 3, 673--696 (2000; Zbl 0960.65074) Full Text: DOI