Semidefinite programs: New search directions, smoothing-type methods, and numerical results

Motivated by some results for linear programs and complementarity problems, this paper gives some new characterizations of the central path conditions for semidefinite programs. Exploiting these characterizations, some smoothing-type methods for the solution of semidefinite programs are derived. The search directions generated by these methods are automatically symmetric, and the overall methods are shown to be globally and locally superlinearly convergent under suitable assumptions. Some numerical results are also included which indicate that the proposed methods are very promising and comparable to several interior-point methods. Moreover, the current method seems to be superior to the smoothing method recently proposed by Chen and Tseng [Non-interior continuation methods for solving semidefinite complementarity problems, Technical report, Department of Mathematics, University of Washington, Seattle, 1999].