This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity.Expand

This article presents the function revolve, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion and is intended to be used as an explicit “controller” for running a time-dependent applications program.Expand

This tutorial describes the source code modification required for the application of ADOL-C, the most frequently used drivers to evaluate derivatives and some recent developments.Expand

A new approach to constrained optimization that is based on direct and adjoint vector-function evaluations in combination with secant updating is proposed, which avoids the avoidance of constraint Jacobian evaluations and the reduction of the linear algebra cost per iteration in the dense, unstructured case.Expand

With the approach presented, much simpler data access patterns and similar or lower computational counts can be achieved through propagating a family of univariate Taylor series of a suitable degree.Expand

This paper presents the integration schemes that are automatically generated when differentiating the discretization of the state equation using Automatic Differentiation (AD), and shows that they can be seen as discretized methods for the and adjoint differential equation of the underlying control problem.Expand

A new approach for computing a sparsity pattern for a Hessian is presented: nonlinearity information is propagated through the function evaluation yielding the nonzero structure. A complexity… Expand

We present a sequential quadratic programming (SQP) type algorithm, based on quasi-Newton approximations of Hessian and Jacobian matrices, which is suitable for the solution of general nonlinear… Expand

The experimental results show that sparsity exploitation via coloring yields enormous savings in runtime and makes the computation of Hessians of very large size feasible and the results also show that evaluating a Hessian via an indirect method is often faster than a direct evaluation.Expand