Transformed quasi-newton method for unconstrained signomial minimization

Vita.A transformed Quasi-Newton algorithm has been developed for the optimization of unconstrained functions. It is applicable when the function or its gradient vector is in the form of a signomial. The algorithm utilizes the transformation of the gradient vector and the variables to locate the optimal solution. The purpose of the transformation is to reduce the search space and to approximate the gradient vector by better than a first order approximation without having to have a higher than second partial derivative. A Quasi-Newton update technique is developed to approximate the inverse of the second transformed partial derivative matrix. The newly developed algorithm is incorporated into a computer code and its computational effectiveness is determined by comparison with the well known Davidon-Fletcher-Powell algorithm. Thirty-two test problems are used in the comparative analysis which include differing numbers of variables and varying degrees of nonlinearity