Turing Computability of (Non-)Linear Optimization

V. Brattka, M. Ziegler, in: Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 2001, pp. 181–184.

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We consider the classical LINEAR OPTIMIZATION Problem, but in the Turing rather than the RealRAM model. Asking for mere computability of a function's maximum over some closed domain, we show that the common presumptions 'full-dimensional' and `bounded' in fact cannot be omitted: The sound framework of Recursive Analysis enables us to rigorously prove this folkloristic observation! On the other hand, convexity of this domain may be weakened to connectedness, and even NON-linear functions turn out to be effectively optimizable.
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Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01)
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181-184
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Brattka V, Ziegler M. Turing Computability of (Non-)Linear Optimization. In: Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01). ; 2001:181-184.
Brattka, V., & Ziegler, M. (2001). Turing Computability of (Non-)Linear Optimization. In Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01) (pp. 181–184).
@inproceedings{Brattka_Ziegler_2001, title={Turing Computability of (Non-)Linear Optimization}, booktitle={Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01)}, author={Brattka, Vasco and Ziegler, Martin}, year={2001}, pages={181–184} }
Brattka, Vasco, and Martin Ziegler. “Turing Computability of (Non-)Linear Optimization.” In Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 181–84, 2001.
V. Brattka and M. Ziegler, “Turing Computability of (Non-)Linear Optimization,” in Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 2001, pp. 181–184.
Brattka, Vasco, and Martin Ziegler. “Turing Computability of (Non-)Linear Optimization.” Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 2001, pp. 181–84.

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