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A parametric version of the ellipsoid method with space scaling by a scalar parameter λ>0 is considered. For certain values of the parameter λ, it is reduced to the available versions of the ellipsoid method, namely, the Shor, Khachiyan, Nemirovsky, and Yudin ones. The properties of two algorithmic implementations of the parameterized ellipsoid method are proved. The first algorithm is based on updating the asymmetric matrix B, and the second one updates the symmetric matrix H= BBT. The applications of the algorithms for solving convex programming problems and for finding the saddle point of a convex-concave function are described. [ABSTRACT FROM AUTHOR]

A method of efficient analysis and solution of conditionally correct problems, which have a unique solution in the subspace, is proposed. The use of a discrete finite-element model on the entire space to obtain a unique solution on the subspace of the initial variational problem is justified. To find a normal pseudo-solution (or a weighted normal pseudo-solution) of a discrete problem (a system of linear algebraic equations with a sparse symmetric semidefinite matrix), a three-stage regularization method is proposed. This method makes it possible to obtain approximations of these solutions with a predetermined accuracy. Efficient adaptive high-performance algorithms of the specified method have been developed for solving systems of linear algebraic equations with sparse symmetric semi-definite matrices using modern computers with parallel computing. [ABSTRACT FROM AUTHOR]

The cycle of researches on methods of formation of the schedule of movement of aircrafts (PS) on the basis of the classical theory of schedules as the theory of multistage systems proceeds in work. It is shown that the movement of the aircraft is a process without interruptions, because each specific flight at a given time is performed by only one aircraft. In contrast to previous work on the theory of schedules, this study takes into account random factors of influence due to meteorological conditions on the flight path. According to the theory of schedules, the problem of stochastic optimisation of the final sequence of requirements serviced by systems with several devices, with different assumptions about the random nature of their maintenance. It is shown that the weakest assumption about the possibility of implementing a generalized operator, which theoretically translates many requirements into many agreed and executed plans, is the monotonic and unimodal kind of the corresponding functionality of the generated plans under small random influences. The potential of the theory of multistage systems in creating an optimal schedule for medium or large airlines as systems of critical application is researched. The basic requirements for the construction of a mathematical schedule in the form of a process controlled by random events are established. Using mathematical models of scheduling based on the basic data of the current movement of aircraft in the area of the airport or air cluster, we established that when the base airports change their purpose and act as terminal airports of arrival, the corresponding elements of the matrix are inversely symmetric. Additional studies of the properties of inversely symmetric matrices and the influence of additive random components on the stability of optimal solutions are carried out. Based on the method of Saaty analytic hierarchy process, the most suitable indicators of the efficiency of forming the optimal schedule in case of coincidences in the consistency indices of partial priorities, taking into account the advantages of arrival and departure times of passenger flights, are selected and substantiated. The expression for the resulting decomposition efficiency functional as a solution of the problem of multi criteria optimisation by the method of quasi-linear convolution of criteria is derived. [ABSTRACT FROM AUTHOR]

A number of requirements are being put forward for steganographic systems. One of the main requirements is the stability of steganomethods against attacks against embedded messages. The task of ensuring this requirement is not completely solved at this time. This task remains relevant. The main reason is the orientation of the mathematical bases of existing methods to specific attacks against the embedded message. Therefore, most of the existing steganographic methods are effective only for specific small attacks. A new method has been developed that is resistant to disturbing influences. This method uses a digital image as a container. The stability of the method is justified theoretically. This justification is based on the specific properties of matrix blocks singular numbers of the original image. All singular numbers are insensitive to disturbing influences, well conditioned. The maximum singular number significantly exceeds all other singular numbers in most lxl-blocks of the image matrix. Blocks obtained as a result of the standard partition of the matrix. Therefore, the angle between the vector of singular numbers and the first vector of the standard basis of the corresponding space is close to zero. In a vector of singular numbers, they are taken in descending order of their values. It is shown that the stability of the stegano process can be ensured by correcting the maximum singular numbers of container blocks. Such a process corresponds to a sufficient condition for the steganomessage to be insensitive to disturbing influences. The specificity of the singular numbers that is used does not depend on the specific type of attack against the embedded message. Embedding a bit of additional information in the container block is carried out in one of two symmetric matrices. These matrices are mapped to the block matrix by virtual reflection of the upper (lower) triangle relative to the main diagonal. This provides the hidden communication channel capacity 1/lxl bit/pixel. [ABSTRACT FROM AUTHOR]

Binary digital representations often are the reflection of various drafts, industrial charts, layouts, plans and others like that, that in practice can occupy several hundreds megabyte, and sometimes and gigabytes at maintenance without a compression. To date images that is used, as a rule, are kept in formats with losses for the economy of traffic and available space in memory (smartphone or computer). But for engineering charts any losses of information often are impermissible, can result in unforeseeable, terrible consequences. Work is sanctified to development of method of compression of binary digital representations without losses. For providing of possibility of taking advantage of algorithms that work with disperse matrix, the matrix of this image transforms to the symmetric kind. For this purpose two symmetric matrices belong in accordance her by the reflection/of her overhead three-cornered underbody of relatively main diagonal, here the shell of each of the got matrices is determined depending on that, what values of elements (zero or single) are more. The compression of data takes place by reduction of profiles of matrices that answer an image. The algorithm of Cathill-Mackey of organization of tops of counts that is put in accordance to the got symmetric matrices is used for this purpose. Proceeding in the stored binary image takes place with the use of shells and vectors of moving that is kept in an offer chart, two symmetric matrices. Algorithmic realization of the worked out method exceeds on efficiency (from the point of view of clench) the analogical formats of maintenance for binary images, in the matrices of that the amount of zeros/of units exceeds the amount of units/of zeros considerably, and can be used as component part of complex graphic package for work with binary images. [ABSTRACT FROM AUTHOR]

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