Non-interior continuation methods for solving semidefinite complementarity problems

There recently has been much interest in non-interior continuation/smoothing methods for solving linear/nonlinear complementarity problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric positive semidefinite real matrices. These extensions involve the Chen–Mangasarian class of smoothing functions and the smoothed Fischer–Burmeister function. Issues such as existence of Newton directions, boundedness of iterates, global convergence and local superlinear convergence will be studied. Preliminary numerical experience on semidefinite linear programs is also reported.