ABSTRACT
In the far-field problem the reflected directions are identified with points on the unit sphere double-struckS2. The variational formulation of the FFR problem in the weak form Equation described later permits its reduction to a linear programming (LP) problem. In this chapter, the authors present a special discretization of the source radiance and formulate the corresponding LP problem. Finally, they present important general remarks indicating limitations on the applicability of the variational approach. According to the duality theory in optimization it is possible to construct a minimization problem dual to the maximization problem. However, in many optical problems the focal function enters into the expression for the cost. Consequently, the resulting optimization problem is not linear and the known methods can not be directly applied for solving the problem.
