A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Optimal control of multistage systems described by high-index differential-algebraic equations
Computational optimal control
Optimal control of systems described by index two differential-algebraic equations
SIAM Journal on Scientific Computing
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Exploiting Invariants in the Numerical Solution of Multipoint Boundary Value Problems for DAE
SIAM Journal on Scientific Computing
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
SIAM Journal on Numerical Analysis
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
SIAM Journal on Optimization
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We investigate a semi-smooth Newton method for the numerical solution of optimal control problems subject to differential-algebraic equations (DAEs) and mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer-Burmeister function the local minimum principle is transformed into an equivalent nonlinear and semi-smooth equation in appropriate Banach spaces. This nonlinear and semi-smooth equation is solved by a semi-smooth Newton method. We extend known local and global convergence results for ODE optimal control problems to the DAE optimal control problems under consideration. Special emphasis is laid on the calculation of Newton steps which are given by a linear DAE boundary value problem. Regularity conditions which ensure the existence of solutions are provided. A regularization strategy for inconsistent boundary value problems is suggested. Numerical illustrations for the optimal control of a pendulum and for the optimal control of discretized Navier-Stokes equations conclude the article.