An interior-point method for semidefinite programming. (English) Zbl 0853.65066

Helmberg, Christoph; Rendl, Franz; Vanderbei, Robert J.; Wolkowicz, Henry

SIAM J. Optim. 6, No. 2, 342-361 (1996).

Authors’ abstract: We propose a new interior-point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

Reviewer: K.Schittkowski (Bayreuth)

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming

Keywords:

semidefinite programming; max-cut relaxations; interior-point method; graph bisection problems; max-min eigenvalue problems; stable set problem