Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Efficient sensitivity analysis of large-scale differential-algebraic systems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
SIAM Journal on Scientific Computing
Design of new Daspk for Sensitivity Analysis
Design of new Daspk for Sensitivity Analysis
Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation
Applied Numerical Mathematics
Cheap Second Order Directional Derivatives of Stiff ODE Embedded Functionals
SIAM Journal on Scientific Computing
Mathematical Programming: Series A and B
Automatic differentiation of explicit Runge-Kutta methods for optimal control
Computational Optimization and Applications
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One approach to solve optimal control problems by direct methods is the so-called sequential approach or single shooting. Only the control variables are discretized resulting in a nonlinear program (NLP) which can be solved with SQP or interior point methods. This paper presents a new methodology to efficiently provide the Hessian of the Lagrangian of that resulting NLP. The algorithm is based on the second-order adjoint method and introduces the novel concept of composite adjoints to reduce the computational effort of a Hessian evaluation. Though this contribution is for the sake of simplicity restricted to single shooting, the same methodology can also be easily applied to multiple shooting.