A path-following inexact Newton method for PDE-constrained optimal control in BV

Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

An inexact Newton hybrid path-following algorithm for nonlinear programming

In this paper we present a hybrid path-following algorithm that generates inexact Newton steps suited for solving large scale and/or degenerate nonlinear programs. The algorithm uses as a central region a relaxed notion of the central path, called quasicentral path, a generalized augmented Lagrangian function, weighted proximity measures, and a linesearch within a trust region strategy. We appl...

An inexact Newton method for nonconvex equality constrained optimization

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence o...

An Inexact Proximal Path-Following Algorithm for Constrained Convex Minimization

Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a tractable proximity operator and that the convex constraints afford a self-concordant barrier. We provide a new joint treatment of proximal a...

Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems

We address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We present two new preconditioners based on a full block matrix factorization of the Schur complement of the Jacobian matrices, where the active-set blocks are merg...