HYBRID METHODOLOGY OF NONLINEAR GOAL PROGRAMMING

Лазо Рољић

Authors

Лазо Рољић Docent na Ekonomskom fakultetu u Banjoj Luci

Keywords:

Non-linear goal programming, Cobb-Douglas’s production function, Euler’s homogeneous function theorem, Feasible directions method

Abstract

What we demonstrate here is a nonlinear goal-programming (NLCP) algorithm based on original hybrid connection of the modified simplex method of goal programming, gradient method of feasible directions and method of optimal displacement size finding-called HMNLCP. Iterative proceedings are given in five steps: (1) linearizing the set of nonlinear constraints at particular point, (2) solving of normalized linear goal programming problem, (3) feasible direction computation, (4) optimal displacement step length calculating, and (5) check the problem convergence. Our idea was to apply Euler's theorem for the "total" linearization of the nonlinear constraints in the region about the particular point. Owing to Euler's homogenous function theorem, it is possible to apply this methodology to solve the non-linear goal programming problems regardless of whether the nonlinear constraint functions are linearly or positively homogenous.

References

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