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Vol 58, No 1 (2018)
- Year: 2018
- Articles: 10
- URL: https://journal-vniispk.ru/0965-5425/issue/view/11198
Article
Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions
Abstract
This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.
1-37
An Attack–Defense Model with Inhomogeneous Resources of the Opponents
Abstract
Germeier’s attack–defense model is generalized by taking into account the inhomogeneity of the defense resources. It is based on Germeier’s generalized equalization principle, which in the general case of inhomogeneous resources leads to convex constrained minimax problems, which can be solved using the subgradient ascent method.
38-47
Universal Method for Stochastic Composite Optimization Problems
Abstract
A fast gradient method requiring only one projection is proposed for smooth convex optimization problems. The method has a visual geometric interpretation, so it is called the method of similar triangles (MST). Composite, adaptive, and universal versions of MST are suggested. Based on MST, a universal method is proposed for the first time for strongly convex problems (this method is continuous with respect to the strong convexity parameter of the smooth part of the functional). It is shown how the universal version of MST can be applied to stochastic optimization problems.
48-64
Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls
Abstract
An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.
65-77
Numerical Solution of the Problem of Determining the Number and Locations of State Observation Points in Feedback Control of a Heating Process
Abstract
The problem of optimizing the number and locations of state observation points in the feedback control of heating a rod in a furnace is considered. The weighting coefficients determining the importance of each observation point in the current linear control function are also optimized. The synthesis of control functions is reduced to the problem of optimizing parameters for a pointwise loaded parabolic equation, which is solved by applying first-order optimization methods.
78-89
Invariant Manifolds for the Burgers Equation Defined on a Semiaxis
Abstract
Stable nonlocal invariant manifolds for the Burgers equation defined on R+ are constructed. One problem of a boundary control stabilizing the solution of this equation to zero is also studied. Results of numerical experiments are presented.
90-101
102-117
Numerical Simulation of the Flow over a Segment-Conical Body on the Basis of Reynolds Equations
Abstract
Numerical simulation was used to study the 3D supersonic flow over a segment-conical body similar in shape to the ExoMars space vehicle. The nonmonotone behavior of the normal force acting on the body placed in a supersonic gas flow was analyzed depending on the angle of attack. The simulation was based on the numerical solution of the unsteady Reynolds-averaged Navier–Stokes equations with a two-parameter differential turbulence model. The solution of the problem was obtained using the in-house solver HSFlow with an efficient parallel algorithm intended for multiprocessor super computers.
118-129
Polynomial-Time Approximation Algorithm for the Problem of Cardinality-Weighted Variance-Based 2-Clustering with a Given Center
Abstract
A strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters is considered. The solution criterion is the minimum of the sum (over both clusters) of weighted sums of squared distances from the elements of each cluster to its geometric center. The weights of the sums are equal to the cardinalities of the desired clusters. The center of one cluster is given as input, while the center of the other is unknown and is determined as the point of space equal to the mean of the cluster elements. A version of the problem is analyzed in which the cardinalities of the clusters are given as input. A polynomial-time 2-approximation algorithm for solving the problem is constructed.
130-136
On the Motion of Agents across Terrain with Obstacles
Abstract
The paper is devoted to finding the time optimal route of an agent travelling across a region from a given source point to a given target point. At each point of this region, a maximum allowed speed is specified. This speed limit may vary in time. The continuous statement of this problem and the case when the agent travels on a grid with square cells are considered. In the latter case, the time is also discrete, and the number of admissible directions of motion at each point in time is eight. The existence of an optimal solution of this problem is proved, and estimates of the approximate solution obtained on the grid are obtained. It is found that decreasing the size of cells below a certain limit does not further improve the approximation. These results can be used to estimate the quasi-optimal trajectory of the agent motion across the rugged terrain produced by an algorithm based on a cellular automaton that was earlier developed by the author.
137-151