An infeasible interior-point algorithm for linear optimization over Cartesian symmetric cones

Abstract

We investigate the effect of making equivalent transformation for the central path from \(x\diamond s=\mu e\) to \(x\diamond s=\mu v\), and we obtain a new class of search directions in both version of feasible and infeasible interior point algorithms for linear optimization over Cartesian symmetric cones. We propose a new modified infeasible interior-point algorithm based on elimination of the centering steps. Moreover, the proposed algorithm finds an \(\varepsilon \)-optimal solution of the underlying problem in polynomial time complexity and its iteration bound coincides with the best known iteration bound for this class of problems.