TY  - CHAP
A1  - Vaarmann, Otu
T1  - On the Solution of Nonlinear Optimization Problems of High Dimension
N2  - A lot of real-life problems lead frequently to the solution of a complicated (large scale, multicriteria, unstable, nonsmooth etc.) nonlinear optimization problem. In order to cope with large scale problems and to develop many optimum plans a hiearchical approach to problem solving may be useful. The idea of hierarchical decision making is to reduce the overall complex problem into smaller and simpler approximate problems (subproblems) which may thereupon treated independently. One way to break a problem into smaller subproblems is the use of decomposition-coordination schemes. For finding proper values for coordination parameters in convex programming some rapidly convergent iterative methods are developed, their convergence properties and computational aspects are examined. Problems of their global implementation and polyalgorithmic approach are discussed as well.
KW  - Nichtlineare Optimierung
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3669
ER  - 
TY  - JOUR
A1  - Vaarmann, Otu
T1  - A class of rapidly convergent interative Methods for Problems in mathematical Modelling
N2  - Methods with the convergence order p 2 (Newton`s, tangent hyperbolas, tangent parabolas etc.) and their approximate variants are studied. Conditions are presented under which the approximate variants preserve their convergence rate intrinsic to these methods and some computational aspects (possibilities to organize parallel computation, globalization of a method, the solution of the linear equations versus the matrix inversion at every iteration etc.) are discussed. Polyalgorithmic computational schemes (hybrid methods) combining the best features of various methods are developed and possibilities of their application to numerical solution of two-point boundary-value problem in ordinary differential equations and decomposition-coordination problem in convex programming are analyzed.
KW  - Mathematisches Modell
KW  - Dialogsystem
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-5223
ER  -