This gives a search direction which can be used in a iterative scheme to ensure good agreement between the linear-quadratic and the nonlinear model. Readings for this topic Dynamic optimization: Discrete Time Dynamic optimization: Continuous Time Math. Thus, at each iteration, the optimal solution is found for the linear-quadratic approximate model. View 2225ch2slideswithfigures.pdf from ECON 2225 at The University of Hong Kong. The dynamic linear-quadratic model has a single analytical optimal control solution, and is thus accurately and effectively solved. This is closely related to the dynamic optimization method based on a combination of a SQP solver and total discretization of the dynamic system. As in SQP, a problem with linear constraints and quadratic objective function is solved iteratively. There are methods which make use of the optimality conditions for dynamic systems (Pontryagin Minimum Principle) just as SQP methods use the Kuhn-Tucker conditions. This as opposed to the well known methods which discretize controls (and states) to transform the problem into a NLP framework.Īn obstacle for its use has been the extensive symbolic manipulations needed to derive the optimality equations for a specific problem, and the difficulty of solving the resulting nonlinear two point boundary value problem. The optimum principle for dynamic systems as formulated by Pontryagin in 1962 may be used for development of numerical algorithms to solve dynamic optimization problems.
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