By use of the equations above, cost is translated into a definite multivariable function of parameters Rr. RG, and A,—AK: The optimal SPS configuration, operating at the lowest electricity cost and predetermined environmental standards, is then found by performing a multivariable iteration to find the least cost combination of taper shapes, antenna and rectenna dimensions, transmit power, etc. METHOD OF SOLUTION («) Optimization The Davidon-Fletcher-Power (DFP) penalty method is a way of determining the local minimum of a function,/(x), where .r is an n-dimensional parameter vector, subject to vector equality and inequality constraints, g(x) = 0 and h(x) 0 (9). The method finds the minimum of a quadratic function in n one-dimensional search steps which are conjugate with respect to a matrix containing second partial derivative information. The particular DFP computer approach used is an excellent algorithm due to Johnson (10). The DFP method requires computation of (a) a penalty function which is the sum of cost function and adjoined inequality constraints as given by Eq. 10, and (b) the gradient of the penalty function with respect to the n parameters of.r, i.e., Rh RG, and At- ANK. In the SPS problem, since the cost function requires evaluating Bessel functions and a quadrature, the respective gradients are determined numerically using a central difference method. The DFP scheme then iteratively generates the approximate inverse of the Hessian matrix (initially chosen as any positive definite matrix, usually an identity matrix) in n-iterations by the accuracy of one-dimensional searches along the gradient of the penalty function which locate a directional minimum by a cubic fit or golden section approach. (b) Inequality Constraints Inequality constraints are adjoined to the cost function by positive penalty constraints. For example, consider the ionosphere inequality contraint defined in Eq. 10,
RkJQdWJsaXNoZXIy MTU5NjU0Mg==