augmented systems – Optimization Online

Iterative Solution of Augmented Systems Arising in Interior Methods

Published: 2005/08/31, Updated: 2007/03/20

Constrained Nonlinear Optimization augmented systems, conjugate gradient method, interior methods, iterative methods, kkt systems, large-scale nonlinear programming, nonconvex optimization, preconditioning

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

Published: 2003/01/20, Updated: 2003/07/01

Kim-Chuan Toh

Semi-definite Programming augmented systems, conjugate residual method, interior point methods, large scale semidefinite programming, maximum clique problem, preconditioners, symmetric quasi-minimal residual method

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