On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems

On the Superlinear Convergence of Interior-Point Algorithms for a General Class of Problems

On a General Class of Interior-point Algorithms for Semideenite Programming with Polynomial Complexity and Superlinear Convergence

We propose a uniied analysis for a class of infeasible-start predictor-corrector algorithms for semideenite programming problems, using the Monteiro-Zhang uniied direction. The algorithms are direct generalizations of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. We show that the algorithms belonging to this class are globally convergent, provided the problem has a so...

On Superlinear Convergence of Infeasible Interior-Point Algorithms for Linearly Constrained Convex Programs

This note derives bounds on the length of the primal-dual affine scaling directions associated with a linearly constrained convex program satisfying the following conditions: 1) the problem has a solution satisfying strict complementarity, 2) the Hessian of the objective function satisfies a certain invariance property. We illustrate the usefulness of these bounds by establishing the superlinea...

A Superlinear Infeasible-Interior-Point Algorithm for Monotone Complementarity Problems

We use the globally convergent framework proposed by Kojima, Noma, and Yoshise to construct an infeasible-interior-point algorithm for monotone nonlinear complemen-tarity problems. Superlinear convergence is attained when the solution is nondegener-ate and also when the problem is linear. Numerical experiments connrm the eecacy of the proposed approach.

Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming