We consider some problems with a set-valued mapping, which can be reduced to minimization of a homogeneous Lipschitz function on the unit sphere. Latter problem can be solved in some cases with a first order algorithm - the gradient projection method. As one ofthe examples, the case when set-valued mapping is the reachable set of a linear autonomous controlled system is considered. In several settings, the linear convergence is proven. The methods used in proofs follow those introduced by B.T. Polyak for the case where Lezanski-Polyak-Lojasiewicz condition holds. Unlike algorithms that use approximation of the reachable set, the proposed algorithms depend far less on dimension and other parameters of the problem. Efficient error estimation is possible. Numerical experiments confirm the effectiveness of the considered approach. This approach can also be applied to various set-theoretical problems with general set-valued mappings.

Abstract— by changing the parameter of the pseudo-random optimization process of the neural network, we generate several variants of training the neural network when solving the classification problem. From them, we obtain bagging — an average solution less susceptible to overfitting. We give an example of performing such bagging and compare it with the classification method based on the Anderson discriminant function and the identically related posterior probability of the class.

The problem of constructing a plan for heterogeneous cargo by unmanned aerial vehicles, with the objective of minimizing transportation time while adhering to the constraints imposed by the capacity of the route network, is addressed. An optimization model is constructed, and a methodology for finding the optimal plan is proposed

This paper further develops the topic of the authors’ previous research. In particular, order statistics of the discrete normalized spectral distribution of the additive white Gaussian noise are investigated to detect a deterministic useful signal in a noise mixture using information features. An additional relationship is established between the discrete spectral distribution of the single-window realization statistics of the white noise. Another novel result consists in exact formulas for calculating the mean and variance of normalized order statistics. Based on the analytical expressions derived, a new formula for calculating the spectral complexity is proposed and the already known one is refined. The theoretical results are verified by statistical simulation.

It is shown that most marsquakes epicenters are located in the zones of extension and fairly high shear stresses associated with deviation of the planet from hydrostatic equilibrium. In this paper, nonhydrostatic stresses in the interior of Venus are calculated for two types of models: an elastic model and a model with a lithosphere of variable thickness (150–500 km) covering a weakened layer that has partially lost its elastic properties. Numerical modeling of the system of elastic equilibrium equations for a gravitating planet is carried out with a step of 1° × 1° degrees in latitude and longitude down to a depth of 480 km, which is the first phase transition in the mantle. The boundary conditions of the problem are the topography and the gravitational field of the planet. In general, the level of nonhydrostatic stress on Venus is not very high. On the surface and in the crust, the highest shear stresses are observed in the region of the Maxwell Montes on Ishtar Terra. Beneath the Maxwell Montes, shear stresses in the crust reach 80 MPa and compressive stresses, 125–150 MPa, depending on the model. Tensile stresses around this area are about 20 MPa. The highest tensile stresses occur in the regions beneath such structures as Lavinia Planitia, Sedna Planitia, and Aino Planitia.