A Note on the Implementation of an Interior-Point Algorithm for Nonlinear Optimization with Inexact Step Computations

This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis et al. (SIAM J Sci Comput 32:3447–3475, 2010), a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in order to … Read more

Automatically Assessing the Performance of an Optimization-Based Multigrid Method

Many large nonlinear optimization problems are based upon discretizations of underlying function spaces. Optimization-based multigrid methods—that is, multigrid methods based on solving coarser versions of an optimization problem—are designed to solve such discretized problems efficiently by taking explicit advantage of the family of discretizations. The methods are generalizations of more traditional multigrid methods for solving … Read more

Data Assimilation in Weather Forecasting: A Case Study in PDE-Constrained Optimization

Variational data assimilation is used at major weather prediction centers to produce the initial conditions for 7- to 10-day weather forecasts. This technique requires the solution of a very large data-fitting problem in which the major element is a set of partial differential equations that models the evolution of the atmosphere over a time window … Read more

Primal-dual interior point methods for PDE-constrained optimization

This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q