Optimization of distributed parameter systems with a combined statistical-deterministic method

This paper describes an optimization method for nonlinear systems with properties that depend on functions instead of discrete parameters. The method is applied to the design of systems with spatially distributed parameters. The underlying mathematical problem of the calculus of variations is approximated by a finite dimensional constrained nonlinear minimax-problem. This is solved with a method that combines a deterministic algorithm for local optimisation with a statistical method for global optimization. The former is based on linearization and linear programming with adaptive trust region, while the latter uses elements from genetic methods and pattern recognition. An example with a nonlinearly loaded nonuniform transmission line shows the capability of the algorithm to determine the unknown optimum function with high precision