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1

The p-Factor Method for Nonlinear Optimization

Szczepanik E.., Prusińska A., Tret’yakov A.

Schedae Informaticae

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2012

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Vol. 21

141--157

EN

We present the main concept and results of the p-regularity theory (also known as p-factor analysis of nonlinear mappings) applied to nonlinear optimization problems. The approach is based on the construction of p-factor operator. The main result of this theory gives a detailed description of the structure of the zero set of irregular nonlinear mappings. Applications include a new numerical method for solving nonlinear optimization problems and p- order necessary and sufficient optimality conditions. We substantiate the rate of convergence of p-factor method.

2

On existence of solutions to nonlinear equations with degenerate mappings

Prusińska A., Tret'yakov A.

Journal of Mathematics and Applications

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2006

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Vol. 28

101-111

EN

The paper presents recent advances in p-regularity theory. The main result of this theory gives a detailed description of the structure of the zero set of an irregular nonlinear mapping. We illustrate the theory with an application to the problem of existence of the solutions to the nonlinear equations with singular mappings.

3

Struktura rozproszonego systemu nauczania (multi-agent learning system) i jego zastosowanie w szkoleniu pilotów

Popov O., Lalanne R., Gouarderes G., Minko A., Tretyakov A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2001

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z. 56[186], t.2

367-374

PL

W artykule rozpatruje się problem stworzenia automatyzowarrych systemów treningowych oraz ich zastosowania w aeronautyce. Przeanalizowano oraz usystematyzowano podejście do opracowania architektury takich systemów bazujących na zastosowaniu metod teorii i techniki sztucznej inteligencji. Opracowano strukturę rozproszonego systemu sztucznej inteligencji (multi-agent system) wykorzystywanego w procesie nauczania. Przedstawione są możliwości zastosowania takiego systemu do nauczania kadry lotniczej.

EN

The problem of creation of the distributed tutoring system and their application in aviation is the subject of this article. The approaches to the design of tutoring systems architecture, based on the artificial intelligence methods, are analysed and classified. The structure of a multiagent tutoring system is proposed. Some approaches to construction and transformations of the aircraft's dynamic models intended for use in simulators are considered.