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Solving discretized degenerate optimal control problems with state constraints

Avelino, Catarina P.

Optimal Control Applications & Methods, 31(3) (2010), 187-199

In this paper, we consider a class of nonlinear optimization problems that arise from the discretization of optimal control problems with bounds on both state and control variables. We are particularly interested in degenerate cases, i.e. when the linear independence constraint qualification is not satisfied. For these problems, we analyse the basic global convergence properties and the numerical behaviour of a multiplier method that updates multipliers corresponding to inequality constraints instead of dealing with multipliers associated with equality constraints. Numerical results obtained for several instances of a discretized optimal control problem governed by a semi-linear elliptic equation are included and indicate that this method is robust on degenerate cases, compared with other nonlinear optimization solvers.