Strona główna UŁ Department of Algorithms and Databases
Faculty of Mathematics and Computer Science
90-238 Łódź, ul.Banacha 22

RESEARCH AND OTHER INTERESTS

NUMERICAL ANALYSIS (NUMERICAL METHODS)
the algorithms for solving nonlinear/nonsmooth equations and applications
the methods for solving optimization problems
the approximation of the generalized Jacobian and B-differential
PROGRAMMING OF NUMERICAL ALGORITHMS
better or worse known programming languages: Pascal, C/C++, Java, Logo, Fortran
XML TECHNOLOGIES
XML (XPath, XPointer, XLink, ...), XSL (XSLT, XSL-FO), XHTML (HTML) and CSS, XML query languages (XQuery, SQL/XML) and other technologies
DATABASES
the relational database management systems (MS Access, MS SQL Server)
relational query languages (SQL, Transact-SQL)
the native XML databases (eXist)
implementations XML standards in DBMS
OPTIMIZATION (MATHEMATICAL PROGRAMMING)
optimization problems, in particular with nonsmooth functions (generalized convexity and the generalized linearity)

ACTIVITIES

SPEAKER IN CONFERENCES AND WORKSHOPS
September 201125th IFIP TC7 Conference on System Modelling and Optimization, Berlin, Germany - An inexact generalized Newton based B-differential method for solving unconstrained LC1 optimization problems
February 2011Congreso de la Real Sociedad Matemática Española 2011, Ávila, Spain - An exponential iterative method for solving nonsmooth equations
October 2010Information Systems in Management 2010, Warsaw, Poland - Indexing XML data and the performance of XQuery in relational database based on SQL Server 2008
October 2009Information Systems in Management 2009, Warsaw, Poland - Efficiency of XQuery in processing native XML data stored in relational database
March 2009Fourth German Polish Conference on Optimization Methods and Applications, Moritzburg, Germany - A perturbed version of an inexact generalized Newton method for solving nonsmooth equations
February 2009Congreso de la Real Sociedad Matemática Española 2009, Oviedo, Spain - Inexact generalized Newton method with scaled residual control
November 2008III Jornadas de Análisis Numérico y Aplicaciones, Logroño, Spain - Inexact generalized Newton methods for solving some special types of nonsmooth equations
September 20089th Congress of SIMAI, Rome, Italia - Some quadrature-based versions of generalized Newton method for solving nonsmooth equations
October 2007Information Systems in Management 2007, Warsaw, Poland - XQuery language and other technologies of XML data querying in relational database based SQL Server
July 2007First French-Spanish Congress of Mathematics, Saragosse, Spain - On a parametrization of generalized Jacobian based Newton method for nonsmooth equations
May 2007Methods and tools of software developing, Szklarska Poręba, Poland - Selected aspects of managing XML data and XQuery language in relational database systems based on SQL Server
September 2002French-German-Polish Conference on Optimization, Cottbus, Germany - New versions of approximate Newton methods for nonsmooth equations
REVIEWER
Applied Mathematical Letters
Applied Numerical Mathematics
Computers and Mathematics with Applications
European Journal of Operational Research
Indian Journal of Mathematics
International Journal of Computer Mathematics
Journal of Optimization, Theory and Applications
Mathematical Modelling and Analysis
Mathematics in Computer Science
Numerical Algorithms
SIAM Journal on Optimization

RESEARCH PAPERS

JOURNAL ARTICLES, REFEREED ARTICLES IN BOOKS & CONFERENCE PAPERS

  1. A note on characterization of solution sets for some nonlinear programming problems - published online in Applicable Analysis (DOI: 10.1080/00036811.2011.584184) (previous version - preprint 12/2003, Faculty of Mathematics, University of Lodz);
  2. Some superlinearly convergent inexact quasi-Newton method for solving nonsmooth equations - Optimization Methods & Software, Vol. 27 No. 3 (2012), 405-417 (previous version - preprint 11/2006, Faculty of Mathematics, University of Lodz);
  3. Some quadrature-based versions of the generalized Newton method for solving nonsmooth equations - Journal of Computational and Applied Mathematics, Vol.235 No.17 (2011), 5131-5139 (previous version - preprint 15/2008, Faculty of Mathematics and Computer Science, University of Lodz);
  4. An approximate Newton method for equations with infinite max functions - International Journal of Computer Mathematics, Vol.88 No.11 (2011), 2403-2414;
  5. Convergence of an inexact generalized Newton method with a scaled residual control - Computers & Mathematics with Applications, Vol.61, No.6 (2011), 1624-1632;
  6. An experimental study on XML data processing efficiency in RDBMS based on SQL Server, in: Information Technology in Management and Marketing, M.Kubina et al. (eds.), EDIS, University Publishing House, Žilina 2010, 205-214;
  7. Indexing XML data and the performance of XQuery in relational database based on SQL Server 2008, in: Information Systems in Management VI. Ontologies and Data Base Technologies, P.Jałowiecki, A.Orłowski (eds.), WULS Press, Warsaw 2010, 109-120 (slides in polish);
  8. Selected aspects of the integration of XML data with relational data in database systems (co-author M.Drozd), in: Information Systems in Management IV, W.Karwowski, A.Orłowski (eds.), WULS Press, Warsaw 2010, 85-93;
  9. Efficiency of XQuery in processing native XML data stored in relational database (co-author M.Drozd), in: Information Systems in Management IV, W.Karwowski, A.Orłowski (eds.), WULS Press, Warsaw 2010, 75-84 (slides in polish);
  10. Convergence of a generalized Newton and an inexact generalized Newton algorithms for solving nonlinear equations with nondifferentiable terms - Numerical Algorithms, Vol.50 No.4 (2009), 401-415 (previous version - preprint 19/2007, Faculty of Mathematics and Computer Science, University of Lodz);
  11. XQuery language and other technologies of data querying in relational database based on SQL Server, in: Information Systems in Management II, A.Jakubiec, W.Karwowski, A.Orłowski (eds.), WULS Press, Warsaw 2008, 144-154 (slides in polish);
  12. A nonsmooth version of univariate optimization algorithm for locating the nearest extremum - Central European Journal of Mathematics, Vol.6 No.3 (2008), 469-481, (previous version - preprint 7/2005, Faculty of Mathematics, University of Lodz);
  13. Selected aspects of managing XML data and XQuery language in relational database systems based on SQL Server, in: Scientific Conference Proceedings - Methods and Tools of Software Developing, Szklarska Poręba 2007, B.Hnatkowska, Z.Huzar (eds.), Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2007, 321-332 (slides in polish);
  14. Inexact quasi-Newton global convergent method for solving constrained nonsmooth equations - International Journal of Computer Mathematics, Vol.84 No.12 (2007), 1757-1770 (previous version - preprint 12/2006, Faculty of Mathematics, University of Lodz);
  15. On a new class parametrized Newton-like method for semismooth equations - Applied Mathematics and Computation, Vol.193 No.2 (2007), 430-437 (previous version - preprint 06/2006, Faculty of Mathematics, University of Lodz);
  16. A generalized Jacobian based Newton method for semismooth block-triangular system of equations - Journal of Computational and Applied Mathematics, Vol.205 No.1 (2007), 305-313, (previous version - preprint 8/2005, Faculty of Mathematics, University of Lodz);
  17. An approximate Newton method for equations with finite max functions - Numerical Algorithms, Vol.41 No.3 (2006), 219-238;
  18. Kuhn-Tucker type optimality conditions for some class of nonsmooth programming problems - Control and Cybernetics, Vol.32 No.2 (2003), 361-376 (modified version of First order optimality conditions for some nonlinear programming problems with nonsmooth functions, preprint 6/1998, Faculty of Mathematics, University of Lodz);

JOURNAL ARTICLES IN REVIEW, MANUSCRIPTS, THESIS

  1. A perturbed version of an inexact generalized Newton method for solving nonsmooth equations - manuscript, submitted for Numerical Algorithms;
  2. A note on approximate Newton methods for nonsmooth equations - preprint 10/2000, Faculty of Mathematics, University of Lodz;
  3. A new versions of approximate Newton method for solving nonsmooth equations (in polish) - Ph.D. thesis, Faculty of Mathematics, University of Lodz, 1999;

RECENT RESEARCH WORKS

NUMERICAL ANALYSIS (in alphabetical order)
A generalized Jacobian based Newton method for semismooth banded block diagonal system of equations - abandoned (bad idea ?) :(
A new modified approximate Secant-type method for univariate unconstrained optimization - a new idea (promising numerical tests under way) ;)
An inexact generalized Newton based B-differential method for solving LC1 unconstrained optimization problems - under way
On some new exponential iterative method for solving nonsmooth equations - under way (promising numerical tests)
Some nonsmooth version of Gauss-Newton method for the nonlinear complementarity problem - under way
COMPUTER SCIENCE
Applications of numerical algorithms in systems supporting XQuery with integration with SVG - still only idea