Equality constraints are dealt with by including them directly in the inner optimization problem of the MBF method. Exact Hessian and gradient information is used throughout all implementations. The MBF, as implemented, consists of a two-stage approach: an outer cycle where the Lagrange multipliers for simple bound constraints of the variables are updated and an inner cycle, where the resulting equality-only constrained nonlinear optimization problem is solved. At present, inequalities in the problem are converted to equalities with the addition of bounded slack variables, the subsequently solved as such. In addition, sparsity is exploited in the overall problem Jacobians. The advantages of the MBF method are demonstrated with test cases coming from the standard literature of process systems engineering. It is also observed that the solutions are attained in few iterations and function evaluations. This work also presents a rigorous approach for the solution of inequality path constrained optimal control problems (OCPs). The scheme uses the MBF method to derive a globally smooth transformation for the inequality path constraint which generates the Euler-Lagrange multiplier trajectories iteratively. It also introduces into discretization methods a novel scheme which is e-convergent with respect to satisfying the path constraints globally. This results in a derived sequence of OCPs that will converge to a prescribed accuracy within a finite number of iterations. Another important development is the initialization of the Lagrange multipliers using only a sparsely discretized path constraint over a time horizon. The method is shown to be effective and promising for future applications in both discretization/collocation and control vector parameterization implementations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:597538 |
| Date | January 2003 |
| Creators | Chen, W. C. T. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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