Abstract:
Dynamic optimization problems arise when coupling an constrained
optimization problem with ordinary differential equations.
We present a numerical method for the resolution of a dynamic optimization
problem arising in the modeling of the dynamics of atmospheric aerosol
particles.
The global optimization problem contains equality and inequality constraints and is treated with a primal-dual interior-point method. The ordinary differential equations are coupled with the KKT system of nonlinear equations expressing the first order optimality conditions. Implicit schemes are used for the time-discretization of the resulting differential-algebraic system.
When considering optimization problems with inequality constraints, the activation or deactivation of these constraints induce discontinuities in the time evolution of the variables. Warm-start techniques do not detect such events accurately and usually compute branches of local minima. Tracking techniques (event location techniques) to locate the times of activation/deactivation of constraints are therefore proposed for the computation of the branches of global minima. Convergence results for the tracking algorithm are given in particular cases. Numerical results are presented for organic atmospheric aerosol particles.
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