Other Nonlinear Options

The following general background may assist you in understanding how the Estimates, Derivatives and Search options are used. For more information, consult the academic papers on the GRG method listed under "Further Reading."

On each major iteration, the GRG Solver must compute values for the first partial derivatives of the objective and constraints. The Derivatives option is concerned with how these partial derivatives are computed.

The GRG (Generalized Reduced Gradient) solution process proceeds by first "reducing" the problem to an unconstrained optimization problem, by solving a set of nonlinear equations for certain variables (the "basic" variables) in terms of others (the "nonbasic" variables). Then a search direction (a vector in N-space, where N is the number of nonbasic variables) is chosen along which an improvement in the objective function will be sought. The Search option is concerned with how this search direction is determined.

Once a search direction is chosen, a one-dimensional "line search" is carried out along that direction, varying a step size in an effort to improve the reduced objective. The initial estimates for values of the variables which are being varied has a significant impact on the effectiveness of the search. The Estimates option is concerned with how these estimates are obtained.