Abstract
We present a theory of quasi-consistent approximations that combines the theory of consistent approximations with the theory of algorithm implementation, presented in Polak (1997), and enables us to solve infinite-dimensional optimization problems whose discretization involves two precision parameters. A typical example of such a problem is an optimal control problem with initial and final value constraints. The theory includes new algorithm models that can be used with two discretization parameters. We illustrate the applicability of these algorithm models by implementing them using an approximate steepest descent method and applying it them to a simple two point boundary value optimal control problem. Our numerical results (not only the ones in this paper) show that these new algorithms perform quite well and are fairly insensitive to the selection of user-set parameters. Also, they appear to be superior to some alternative, ad hoc schemes.
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Pironneau, O., Polak, E. (2005). On a Quasi-Consistent Approximations Approach to Optimization Problems with Two Numerical Precision Parameters. In: Qi, L., Teo, K., Yang, X. (eds) Optimization and Control with Applications. Applied Optimization, vol 96. Springer, Boston, MA. https://doi.org/10.1007/0-387-24255-4_20
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DOI: https://doi.org/10.1007/0-387-24255-4_20
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