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A spectral bundle method for semidefinite programming. (English) Zbl 0960.65074

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.

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

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