Optimization with Restriction in the Generalized Phase Problem

The optimization problems with restriction on the amplitude of objective functions are considered. Such kind of problems concerns to the inverse (synthesis) problems according to the amplitude characteristics and belongs to the optimization problems with the incomplete input data. The variational statement foresees the deriving respective Euler equation of the optimizing functional or the systems of such equations. Due to specific of statement of problems, the derived Euler equations are nonlinear ones and have non-unique solution. Three types of such solutions are extracted and their properties and branching is investigated numerically. The numerical results are discussed for different kind of input data.