Models and Methods for Three External Ballistics Inverse Problems

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 epsilon-Lipschitz ones. We have constructed a unified numerical method to solve these problems based on the algorithm of projecting a point onto epsilon-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; epsilon-Lipschitz; projection onto nonconvex set; approximate solution.

References

1. Konovalov A.A. Vneshnyaya ballistika [External Ballistics]. Мoscow, Tsentral'nyy nauchno-issledovatel'skiy institut informacii, 1979. (in Russian)
2. Arutyunova N.K., Dulliev A.M., Zabotin V.I. Algorithms for Projecting a Point onto a Level Surface of a Continuous Function on a Compact Set. Computational Mathematics and Mathematical Physics, 2014, vol. 54, no. 9, pp. 1395-1401. DOI: 10.7868/S0044466914090038
3. Zabotin V.I., Arutyunova N.K. [Two Algorithms for Finding the Projection of a Point onto a Nonconvex Set in a Normed Space]. Computational Mathematics and Mathematical Physics, 2013, vol. 53, no. 3, pp. 344-349. DOI: 10.7868/S0044466913030162 (in Russian)
4. Vanderbei R.J. Extension of Piyavskii's Algorithm to Continuous Global Optimization. Journal of Global Optimization, 1999, vol. 14, pp. 205-216.
5. Nesterov Yu. Vvedenie v vypukluyu optimizaciyu [Introduction into a Convex Optimization]. Мoscow, Moskovskiy tsentr nepreryvnogo matematicheskogo obrazovaniya, 2010. (in Russian)
6. Arutyunova N., Dulliev A., Zabotin V. Models and Methods for Three External Ballistics Inverse Problems. Available at: http://arxiv.org/abs/1610.02933 (accessed 16 October 2017).