Abstract

A simple homogeneous primal-dual feasibility model is proposed for semidefinite programming (SDP) problems. Two infeasible-interior-point algorithms are applied to the homogeneous formulation. The algorithms do not need big M initialization. If the original SDP problem has a solution, then both algorithms find an ffl-approximate solution (i.e., a solution with residual error less than or equal to ffl) in at most O( p n ln(ae ffl 0 =ffl)) steps, where ae is the trace norm of a solution and ffl 0 is the residual error at the (normalized) starting point. A simple way of monitoring possible infeasibility of the original SDP problem is provided such that in at most O( p n ln(aeffl 0 =ffl)) steps either an ffl-approximate solution is obtained, or it is determined that there is no solution with trace norm less than or equal to a given number ae ? 0. Key Words: semidefinite programming, homogeneous interior-point algorithm, polynomial complexity. Abbreviated Title: Homogeneous al...

Citations