Convergence Analysis of an Inexact Infeasible Interior Point Method for Semidefinite Programming
Computational Optimization and Applications
Solving semidefinite programming problems via alternating direction methods
Journal of Computational and Applied Mathematics
A relaxed cutting plane method for semi-infinite semi-definite programming
Journal of Computational and Applied Mathematics
Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
Optimization Methods & Software
Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step
Numerical Algorithms
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A primal-dual infeasible-interior-point path-following algorithm is proposed for solving semidefinite programming (SDP) problems. If the problem has a solution, then the algorithm is globally convergent. If the starting point is feasible or close to being feasible, the algorithm finds an optimal solution in at most $O(\sqrt{n}L)$ iterations, where n is the size of the problem and L is the logarithm of the ratio of the initial error and the tolerance. If the starting point is large enough, then the algorithm terminates in at most O(nL) steps either by finding a solution or by determining that the primal-dual problem has no solution of norm less than a given number. Moreover, we propose a sufficient condition for the superlinear convergence of the algorithm. In addition, we give two special cases of SDP for which the algorithm is quadratically convergent.