Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction

[摘要] We prove the theoretical convergence of a short-step, approximatepath-following, interior-point primal-dual algorithm forsemidefinite programs based on the Gauss-Newton directionobtained from minimizing the norm of the perturbed optimalityconditions. This is the first proof of convergence for theGauss-Newton direction in this context. It assumes strictcomplementarity and uniqueness of the optimal solution as well asan estimate of the smallest singular value of the Jacobian.

[学科分类] 应用数学