Thus the problem of finding the complex function A(/?)e1*,(W has been reduced to the problem of finding the real coefficients xn and yn accordingly to the requirements for SPS characteristics. The method of penalty functions, although rather tedious, is the most universal method for solving this problem. Making use of non-linear parametric optimization techniques, it involves finding values for the coefficients which minimize the penalty function which reflects the problem given. For example, in the problem of maximizing collection efficiency the penalty function is: In the problem of minimizing the electricity cost with constraints for sidelobe levels and maximum power density at the antenna the penalty function can be written as:
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