Geodesic
Models and methods for three external ballistics inverse problems
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 78-91

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We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semi-axis position) when firing an unguided artillery projectile on the assumption that the gun barrel semi-axis can move in a connected nonconvex cone having a non-smooth lateral surface and modelling visibility zone restrictions. In the first problem, the target is in the true horizon plane of the gun, the second and the third problems deal with some region of 3D space. A distinctive feature of the models is that the objective functions are $\varepsilon$-Lipschitz ones. We have constructed a unified numerical method to solve these problems based on the algorithm of projecting a point onto $\varepsilon$-Lipschitz level function set. A computer programme has been based on it. А series of numerical experiments on each problem has been carried out.
Keywords: mathematical modelling; inverse problem of external ballistics; optimization; $\varepsilon$-Lipschitz; projection onto nonconvex set; approximate solution. 
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     author = {N. K. Arutyunova and A. M. Dulliev and V. I. Zabotin},
     title = {Models and methods for three external ballistics inverse problems},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a7/}
}
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N. K. Arutyunova; A. M. Dulliev; V. I. Zabotin. Models and methods for three external ballistics inverse problems. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 78-91. http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a7/