On the Solution of Nonlinear Optimization Problems of High Dimension

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.