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Towards decomposition of large optimization problems in machine dynamics. (English) Zbl 0818.90101

Summary: The large polyoptimization problem may be considered as a set of interacted partial subproblems. The subproblems can be solved separately but it is possible to find not only one optimum for each subproblem but for the whole system as well. It requires the use of coordination techniques.
Many machine dynamics problems can be described as large decomposed problems. The decomposition results from the multi-aspect character of machine dynamics problems. The main purpose of the decomposition is the replacing of the global problem by the set of the interconnected subproblems. The solution with the help of polyoptimization methods is relatively easier.
The numerical methods for solving every subproblem depend on the form of the state equations (discrete, continuous, linear, nonlinear), external disturbances (deterministic, stochastic), parameters (deterministic, random) and also the information which is needed. All these methods allow to extend the range of analysis in two directions: (1) the problem size extension, (2) the extension number of variants.
The first trend is often practically realized. The other one is connected with the data processing in the selection of the output data. The application of polyoptimization methods is the natural way of solving such problems.

MSC:

90C29 Multi-objective and goal programming
90C06 Large-scale problems in mathematical programming
70E15 Free motion of a rigid body
93A15 Large-scale systems
76Q05 Hydro- and aero-acoustics
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