The Radiation Transfer at a Layer of Magnetized Plasma With Random Irregularities

The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The small-angle scattering approximation in the invariant ray coordinates is suggested for analytical investigation of the radiation transfer equation. The approximated solution describing spatial-and-angular distribution of radiation reflected from a plasma layer has been obtained. The obtained solution has been investigated numerically for the case of the ionospheric radio wave propagation. Two effects are the consequence of multiple scattering: change of the reflected signal intensity and anomalous refraction.Comment: 22 pages, 4 figure

On the implementation of some methods applied to optimization design problems

It is shown that in optimization problems arising during electronic circuit design constraints often may be represented as a direct product of some sets from different spaces which in general may have different dimensions. Taking into account this form of valid set makes it possible a decomposition of the optimization problem of large dimension. It is also shown that in man-machine decision support systems implemented on parallel computers it is possible to branch the optimization algorithm in order to reduce computing time. The efficiency of the approach is demonstrated by using a modification of gradient and subgradient projection methods for electronic circuit design

A cutting-plane method without inclusions of approximating sets for conditional minimization

© 2015, Pleiades Publishing, Ltd. Propose a cutting-plane method with partially embedding of a feasible set for solving a conditional minimization problem. The proposed method is characterized by possibility of periodically dropping of an arbitrary number of any planes constructed in the solution process. Prove convergence of the method, discuss its features, represent assessments of the solution’s accuracy

Cutting-plane method based on epigraph approximation with discarding the cutting planes

© 2015, Pleiades Publishing, Ltd. Propose a method for solving a mathematical programming problem from the class of cutting methods. In our method, on each step the epigraph of the objective function is embedded into a specifically constructed polyhedral set, and on this set an auxiliary linear function is minimized in order to construct the iteration point. Proposed method does not require that each approximation set is embedded in the previous ones. This feature lets us periodically discard additional constraints that form the approximation sets obtained during the solution process. Prove the method’s convergence and discuss possible implementations

Cutting-plane method with embedding of epigraphs of auxiliary functions

© 2017 IEEE. We propose a method of conditional minimization of convex functions from the class of cutting methods. The method based on using of the exterior penalty functions. The iteration points are found by solving linear programming problems. In this case, the admissible set and the epigraph of each auxiliary function are embedded into polyhedral sets. A set, that approximates the epigraph of the next auxiliary function, is constructed on the basis of the previous set by cutting off the iteration point from it. The method's convergence is proved

A Cutting method for finding discrete minimax with dropping of cutting planes

In this paper we propose a cutting method to solve a conditional minimization problem of a discrete maximum function. In the method some polyhedral set approximates the epigraph of the objective function, and to construct the following iteration point we minimize an auxiliary linear function on this set. The method does not imply the inclusion of each of approximating sets in the previous one. This feature allows us to periodically drop any additional restrictions which occur in the solution process. We describe the features of the proposed method and prove its convergence. © 2014 Pleiades Publishing, Ltd

One cutting plane algorithm using auxiliary functions

© Published under licence by IOP Publishing Ltd.We propose an algorithm for solving a convex programming problem from the class of cutting methods. The algorithm is characterized by the construction of approximations using some auxiliary functions, instead of the objective function. Each auxiliary function bases on the exterior penalty function. In proposed algorithm the admissible set and the epigraph of each auxiliary function are embedded into polyhedral sets. In connection with the above, the iteration points are found by solving linear programming problems. We discuss the implementation of the algorithm and prove its convergence

One approach to constructing cutting algorithms with dropping of cutting planes

We propose a general cutting method for conditional minimization of continuous functions. We calculate iteration points by partially embeddimg the admissible set in approximating polyhedral sets. We describe the features of the proposed method and prove its convergence. The constructed general method does not imply the inclusion of each of approximating sets in the previous one. This feature allows us to construct cutting algorithms which periodically drop any additional restrictions which occur in the solution process. © 2013 Allerton Press, Inc

A minimization method with approximation of feasible set and epigraph of objective function

© 2016, Allerton Press, Inc.For a convex programming problem we propose a solution method which belongs to the class of cutting-plane methods. When constructing approximate solutions to the problem, this technique concurrently approximates its feasible set and the epigraph of the objective function. Planes for cutting the iteration points are being constructed with the help of subgradients of the objective function and left-hand sides of constraints. In this connection, one can find each iteration point by solving a linear programming problem. As distinct from most other well-known cuttingplane methods, the proposed technique allows the possibility to periodically update approximating sets by dropping accumulated constraints. We substantiate the convergence of the proposed method and discuss its numerical realization

Peculiarities of anisotropy and polarization as an indicator of noises in the CMB maps

We discuss some new problems of the modern cosmology which arose after the BOOMERANG and MAXIMA-1 successful missions. Statistics of high peaks of the CMB anisotropy is analyzed and we discuss possible inner structure of such peaks in the observational data of future MAP and PLANCK missions. We have investigated geometrical and statistical properties of the CMB polarization around such high isolated peaks of anisotropy in the presence of a polarized pixel noise and point sources. The structure of polarization fields in the vicinity of singular points with zero polarization is very sensitive to the level of pixel noises and point sources in the CMB maps.Comment: 9 pages, 2 figure