A new approach based on parametric linearization technique for solving nonlinear programming problems

Abstract

In this paper, a parametric linearization approach for obtaining an approximate global optimum solution of nonlinear programming (N.L.P) problems is proposed. Especially when the objective and/or the constraints are non-smooth functions, we define a global weak differentiation to make in a sense the non-smooth functions as a new smooth functions. This new definition for weak differentiation enables us to use practically the classic algorithms for non-smooth N.L.P problems. In our approach, we transfer the N.L.P problems to a sequence of linear programming problems defined on the special feasible regions. We prove that the proposed approach is convergent to the global optimum solution of the original N.L.P problem when the norm of the partitions of the feasible region of N.L.P tends to zero. Numerical examples indicate that the proposed approach is extremely robust, and may be used successfully to obtain the approximate solution of a wide range of nonlinear programming problems.