Iterative Solution of Augmented Systems Arising in Interior Methods

Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods define a sequence of KKT equations that represent the symmetrized (but indefinite) equations associated with Newton’s method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dual … Read more

Solving large scale semidefinite programsvia an iterative solver onthe augmented systems

The search directions in an interior-point method for large scale semidefinite programming (SDP) can be computed by applying a Krylov iterative method to either the Schur complement equation (SCE) or the augmented equation. Both methods suffer from slow convergence as interior-point iterates approach optimality. Numerical experiments have shown that diagonally preconditioned conjugate residual method on … Read more