{"user_id":"15415","language":[{"iso":"eng"}],"type":"conference","department":[{"_id":"63"}],"author":[{"full_name":"Brattka, Vasco","last_name":"Brattka","first_name":"Vasco"},{"first_name":"Martin","full_name":"Ziegler, Martin","last_name":"Ziegler"}],"year":"2001","title":"Turing Computability of (Non-)Linear Optimization","date_created":"2020-08-24T11:33:12Z","status":"public","date_updated":"2022-01-06T06:53:26Z","page":"181-184","publication":"Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01)","citation":{"ieee":"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.","chicago":"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.","apa":"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).","short":"V. Brattka, M. Ziegler, in: Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG’01), 2001, pp. 181–184.","bibtex":"@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} }","ama":"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.","mla":"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."},"_id":"18168","abstract":[{"text":"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.","lang":"eng"}]}