Algorithm for construction of parametric vectors for solution of classification problems by a feed-forward neural network

A universal heuristic algorithm is considered that constructs the vector of properties of an object that are distributed among heterogeneous groups. This algorithm is based on a feed-forward neural network. An automatic system for objects classification is described. The use of the automatic classification system for a literary authorship attribution problem is considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 3–14, March–April 2007.     

Pursuit problem in distributed control systems

A pursuit problem in distributed parabolic control systems without mixed derivatives with variable coefficients is considered. The finite-difference method is used to solve this problem. Necessary conditions for the termination of a pursuit are obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 153–158, March–April 2009.     

An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.     

A Continuous problem of optimal partition with a nondifferentiable functional

A continuous problem of decomposition of an optimal set into disjoint subsets is considered. This problem is characterized by a non-differentiable performance criterion, the availability of a boundary-value problem for a parabolic type equation, and dependence of the initial condition function on the partition of some flat set. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 115–125, July–August, 2000.     

A taxation model

A new approach to taxation modeling is considered that takes into account the relationship between the costs of fixed capital and direct labor. The well-known Balatskii model in which the emphasis is put on fixed capital is substantially generalized. The problem of optimizing the total tax rate with respect to a Laffer-type criterion is solved. Statistical data for Ukraine over 2000–2003 are used. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 160–164, January–February 2007.     

Necessary and sufficient optimality conditions of a design decision on the structure of a local computer network

A problem of nonlinear programming with Boolean variables is considered, for which the possibility of extension of the optimality conditions of solving a special problem of nonlinear programming (with continuous variables) is shown by statistical estimation of possible design decisions. This contributed to the solution of the initial problem by simpler methods. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 133–137, September–October, 1999.     

Fokker–Planck approximation of the master equation in molecular biology

The master equation of chemical reactions is solved by first approximating it by the Fokker–Planck equation. Then this equation is discretized in the state space and time by a finite volume method. The difference between the solution of the master equation and the discretized Fokker–Planck equation is analyzed. The solution of the Fokker–Planck equation is compared to the solution of the master equation obtained with Gillespie’s Stochastic Simulation Algorithm (SSA) for problems of interest in the regulation of cell processes. The time dependent and steady state solutions are computed and for equal accuracy in the solutions, the Fokker–Planck approach is more efficient than SSA for low dimensional problems and high accuracy.     

Approximate solution of a nonlinear system of equations for two-phase media

A mixed initial-boundary-value problem for the nonlinear equations describing the dynamic consolidation of water-saturated soils is considered. The error of a time-continuous approximate generalized solution is estimated using the finite-element method. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 73–88, July–August 2008.     

Stability radius of an efficient solution of a vector problem of integer linear programming in the Gölder metric

A vector (multicriterion) problem of integer linear programming is considered on a finite set of feasible solutions. A metric l_p, 1 ≤ p ≤ ∞, is defined on the parameter space of the problem. A formula of the maximum permissible level of perturbations is obtained for the parameters that preserve the efficiency (Pareto optimality) of a given solution. Necessary and sufficient conditions of two types of stability of the problem are obtained as corollaries. This work has been carried out with financial support from the Belgosuniversity within the framework of the Intercollegiate Program “Fundamental and Applied Investigations” (project No. 492/28). __________ Translated from Kibernetika I Sistemnyi Analiz, No. 4, pp. 175–181, July–August 2006.     

A Partial Inverse Linear-Quadratic Optimization Problem

A partial linear-quadratic problem is considered. It is formulated as the determination of the perturbation of a matrix that belongs to a control block under the constraint that the perturbation is such that an extreme value of a quadratic functional has a preassigned form in the “perturbed system” obtained. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 183–188, May–June 2005.     

Stabilization by Local Projection for Convection–Diffusion and Incompressible Flow Problems

We give a survey on recent developments of stabilization methods based on local projection type. The considered class of problems covers scalar convection–diffusion equations, the Stokes problem and the linearized Navier–Stokes equations. A new link of local projection to the streamline diffusion method is shown. Numerical tests for different type of boundary layers arising in convection–diffusion problems illustrate the stabilizing properties of the method.     

A model of optimal control over a nonlinear multidimensional innovation diffusion process

A model of competitive innovation diffusion is considered. The model is based on the Lotka-Volterra system and an initial-boundary problem for a system of quasilinear parabolic equations. The maximum principle is proved for the problem of diffusion of two competitive innovations, and sufficient conditions of existence of optimum control are obtained for the system. A numerical algorithm is constructed for solving optimum control problems, and numerical results for a model example are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 120–133, July–August 2008.     

A Benders Decomposition Method for Solving Stochastic Complementarity Problems with an Application in Energy

In this paper we present a new Benders decomposition method for solving stochastic complementarity problems based on the work by Fuller and Chung (Comput Econ 25:303–326, 2005; Eur J Oper Res 185(1):76–91, 2007). A master and subproblem are proposed both of which are in the form of a complementarity problem or an equivalent variational inequality. These problems are solved iteratively until a certain convergence gap is sufficiently close to zero. The details of the method are presented as well as an extension of the theory from Fuller and Chung (2005, 2007). In addition, extensive numerical results are provided based on an electric power market model of Hobbs (IEEE Trans Power Syst 16(2):194–202, 2001) but for which stochastic elements have been added. These results validate the approach and indicate dramatic improvements in solution times as compared to solving the extensive form of the problem directly.     

Choosing the parameter of a modified additive-averaged splitting algorithm

The problem-solving time and the solution accuracy are expressed as functions of a parameter. An optimization problem of choosing the parameter using a “time cost–solution accuracy” criterion is considered. A Pareto-optimal set of solutions is obtained. The best value of the parameter is chosen by the ideal-point method. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 98–105, July–August 2009.     

Multifactor authentication as a protection mechanism in computer networks

A direction of authentification is considered that is a component of the problem of creating mechanisms for information protection in computing systems (CS). The proposed mechanism of multifactor authentication makes it possible to increase the degree of security of authentication procedures in CS, which is especially important in practice. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 170–175, September–October, 1999.     

Stability criterion for a lexicographic Boolean optimization problem

A vector Boolean sequential minimization problem for absolute values of linear functions is considered. Necessary and sufficient condition for stability of this type that is a discrete analogue of the upper Hausdorff semicontinuity of a point-to-set mapping is established. This mapping associates a set of lexicographic optima with each set of problem parameters. The study was sponsored by the Fundamental and Applied Research Interuniversity Program of the Republic of Belarus (Grant 492/28). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 127–132, July–August 2007.     

Analysis of an algorithm for solution of conditional optimization problems with linear-fractional objective functions over permutations

A method is considered to solve a conditional optimization problem with a linear-fractional objective function over permutations. The performance of sub algorithms to solve this problem is evaluated. The practical efficiency of the algorithm is analyzed by conducting numerical experiments. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 133–146, July–August 2007.     

Efficient difference scheme for numerical solution of a convective diffusion problem

Problems of modeling of atmospheric circulation are investigated. A new method for solution of a one-dimensional nonstationary inhomogeneous initial-boundary-value problem of convective diffusion is considered. The problem is solved using a new unconditionally stable and efficient difference scheme. The results of a theoretical analysis of the scheme are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 64–74, May–June 2007. An erratum to this article is available at .     

An optimal control model for a system of degenerate parabolic integro-differential equations

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 90–102, November–December 2007.     

Mathematical models of some nonlinear systems and their computer realization

A model of an interphase layer in composite media is investigated. Functional spaces are introduced and general operator equations are constructed that include operators of interface conditions in addition to boundary conditions. Projective-iterative methods for solving operator equations in the stationary case are considered. The result of computer realization of an inhomogeneous nonlinear boundary-value problem is illustrated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 76–81, September–October 2008.