Informatica

This paper is devoted to the application of adaptable difference schemes for the simulation of propagation and interaction of focused laser beams. New effective processes for the solution of stationary nonlinear optics problems are proposed. Simulation results on real experiment data show the advantages of such schemes and iteration processes.

In this paper we deal with the problem of extremal parameter grouping. The problem formulation, the algorithms of parameter grouping and the fields of implementation are presented. The deterministic algorithms of extremal parameter grouping often find the local maximum of the functional, characterizing the quality of a partition. The problem has been formulated as a problem of combinatorial optimization and attempted to be solved using the simulated annealing strategy. The algorithms, realizing such a strategy and devoted to the solving of the problem concerned, are proposed and investigated.

A new concept of an exact auxiliary function (EAF) is introduced. A function is said to be EAF, if the set of global minimizers of this function coincides with the global solution set of the initial optimization problem. Sufficient conditions for exact equivalence of the constrained minimization problem and minimization of EAF are provided. The paper presents various classes of EAF for a non linear programming problem, which has a saddle point of Lagra ge function.

In this paper the problem of optimization of multivariate multimodal functions observed with random error is considered. Using the random function for a statistical model of the objective function the minimization procedure is suggested. This algorithm is convergent on a discrete set. To avoid computational difficulties, the modified algorithm is defined by substituting the parameters of minimization procedure by their estimates.

In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.

This paper briefly reviews some of the recent results on the problems and algorithms for their solution in quadratic 0-1 optimization. First, the complexity of problems is discussed. Next, some exact algorithms and heuristics are mentioned. Finally, results in the analysis of the algorithms for 0-1 quadratic problems are summarized. The papers written in Russian are considered more thoroughly here.

The aggregate approach to the formal description, verification and simulation of computer network protocols is considered in the paper. With this approach, the offered design stages can be performed using a single mathematical scheme. The reachability analysis method and the program proof technique are viewed as methods for correctness analysis. The proposed approach for correctness analysis and model construction was used in creating the protocol analysis system PRANAS.

The maximization problem for an objective function f given on a feasible region X is considered, where X is a compact subset of Rⁿ and f belongs to a set of continuous multiextremal functions on X can be evaluated at any point x in X without error, and its maximum M=max x∈Xf(x) together with a maximizer x^*(a point x^* in X such that M=f(x^*)) are to be approximated. We consider a class of the global random search methods, underlying an apparatus of the mathematical statistics and generalizing the so-called branch and bound methods.

The problems and results in constructing the statistical models of multimodal functions are reviewed. The rationality of the search for global minimum is formulated axiomatically and the features of the corresponding algorithm are discussed. The results of some applications of the proposed algorithm are presented.

The role and goals of computer programming in the education of young people are discussed. The activity of the Lithuanian Young Programmers School by correspondence is described. Motivation of its curriculum and the way of teaching are given. Relations with the competitions of programmers and some other forms of teaching are considered.