A convergence analysis for a convex version of Dikin’s algorithm

This paper is concerned with the convergence property of Dikin’s algorithm applied to linearly constrained smooth convex programs. The paper studies a version of Dikin’s algorithm in which a second-order approximation of the objective function is minimized at each iteration together with an affine transformation of the variables. It proves that the sequence generated by the algorithm globally converges to a limit point at a local linear rate if the objective function satisfies a Hessian similarity condition. The result is of a theoretical nature in the sense that in order to ensure that the limit point is an •-optimal solution, one may have to restrict the steplength to the order of O(•). The analysis does not depend on non-degeneracy assumptions.