Vladislav Zabotin | Searcharxiv

arXiv2024

Global optimization of multivariable functions satisfying the Vanderbei condition

We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an $\varepsilon$-Lipschitz continuous function). The algorithms belong to the class of non-uniform cover-ings methods. For the algorithms we prove propositions about convergence to an $\varepsilon$-solution in terms of the objective function. We illustrate the performance of the algorithms using several test numerical examples with non-Lipschitz continuous objective functions.

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arXiv2020

Models and Methods for Three External Ballistics Inverse Problems

We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semiaxis position) when firing an unguided artillery projectile on the assumption that the gun barrel semiaxis 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 an algorithm of projecting a point onto $\varepsilon$-Lipschitz level function set. A computer program has been based on it. A series of numerical experiments on each problem has been carried out. App. 1.

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