Hybrid Methodology of Nonlinear Goal Programming

What we demonstrate here is a nonlinear goal-programming (NGP) algorithm based on hybrid connection of the modified simplex method of goal programming, gradient method of feasible directions and method of optimal displacement size finding-called HNGPM. Iterative methodology is given in five steps: (1) linearization the set of nonlinear constraints at particular point, (2) solving the problem of normalized linear goal programming, (3) feasible direction computation, (4) calculating optimal step length displacement, and (5) testing out convergence problem. Our idea was to apply Euler’s theorem for the “total” linearization of the nonlinear constraints (in the space) around particular point. According to Euler’s theorem, it is possible to apply this methodology to solve the problems of NGP whether the nonlinear constraint functions are linearly or positively homogeneous.