Informatica

This paper is devoted to the construction and investigation of difference schemes for the solution of one-dimensional parabolic problems with non-classical boundary conditions. The stability of schemes and the convergence of a numerical solution is proved in the norms L1 and C.

The paper deals with the minimization algorithms which enable us to economize the computing time during the coordinated calculation of the values of an objective function on the nodes of a rectangular lattice by storing and using quantities that are common for several nodes. The algorithm of a uniform search with clustering, the variable metric algorithm and the polytope algorithm are modified.

The observation problem along with the certain independent value plays a great role while carrying out control of dynamic systems in the conditions of uncertainty (Kalman, 1957, Krasovski, 1985, Leondes, 1976). A new approach on connection between the problems of control and observation is presented in (Gabasov, 1991). Developing it, we justify the solution of observation problem in the given paper that arises, at optimization of linear dynamic systems. The paper consists of the two parts. In the part I the linear discrete system is investigated. In the part II the linear dynamic continuous system is considered.

The principles of a neural network environmental model are proposed. The principles are universal and can use different neural network architectures. Such a model is self-organizing, it can operate in both regimes with and without a teacher. It codes information about objects, their features, the actions operating in an environment, analyzes concrete situations. There are functions for making an action plan, for action control. The goal of the model is given from an external site. The model has more than sixteen active regimes. The neural network environmental model is fulfilled in software and hardware tools.

This paper is concerned with the derivation of open-loop Stackelberg (OLS) solutions of a class of continuous-time two-player nonzero-sum differential games characterized by quadratic cost functionals and linear singular systems. By applying the calculus of variations, necessary conditions are derived under which the open-loop Stackelberg solution of the leader exists. Under the transformation by which the matrix E has diagonal form, we derive a matrix Riccati differential equation from the necessary conditions. An example is given to illustrate the results of the paper.

In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.

The paper considers the analysis technique of the general and individual properties of aggregative specifications. The method is based on constructing a set of axioms describing both the aggregate specifications and the properties of the model under investigation. The resolution method using logical programming language PROLOG is applied in creating the axiom system. An example of aggregative specification analysis for the alternating bit protocol is presented.

In general terms some situations are described which require the exploitation of heuristics either to solve a mathematical optimization problem or to analyse results. A possibility to implement heuristic knowledge for selecting a suitable algorithm depending on available problem data and information retrieved from the user, is investigated in detail. We describe some inference strategies and knowledge representations that can be used in this case, and the rule-based implementation within the EMP system for nonlinear programming. Case studies are presented which outline on the one hand the heuristic recommendation of an optimization code and the achieved numerical results on the other hand.