Fixing Variables in Semide nite RelaxationsChristoph

The standard technique of reduced cost xing from linear programming is not trivially extensible to semideenite relaxations as the corresponding La-grange multipliers are usually not available. We propose a general technique for computing reasonable Lagrange multipliers to constraints which are not part of the problem description. Its specialization to the semideenite f?1;1g relaxation of quadratic 0-1 programming yields an eecient routine for xing variables. The routine ooers the possibility to exploit problem structure. We extend the traditional bijective map between f0;1g and f?1;1g formulations to the constraints such that the dual variables remain the same and structural properties are preserved. In consequence the xing routine can eeciently be applied to optimal solutions of the semideenite f0;1g relaxation of constrained quadratic 0-1 programming, as well. We provide numerical results showing the eecacy of the approach.