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In this paper, a novel solution approach for solving the nonlinear programming (NLP) problems having m nonlinear algebraic inequality (equality or mixed) constraints with a nonlinear algebraic objective function in n variables using linearization technique is presented. This approach performs successive increments to find a solution of the NLP problem, based on the optimal solutions of linear programming (LP) problems, satisfying the nonlinear constraints oversensitively. In the proposed approach, the original problem is converted to the LP problem using increments in the linearization process and the impact of computational efficiency makes the performance of the solution well. It is presented that how the solution approach can be applied to solve the illustrated examples from the literature.

In this paper, we proposed a new iterative approach for solving the nonlinear programming (NLP) problem having n nonlinear (or linear) algebraic equality constraints with nonlinear (or linear) algebraic objective function in n + 1 variables. The advantage of this developed iterative approach is to construct different optimization problems corresponding to the parameter related with arbitrary points which are chosen satisfying the constraints. Solution(s) obtained from constructed optimization problem(s) satisfies the constraints oversensitively. Several numerical examples are given to illustrate the proposed approach.

Nonlinear equations arise frequently while modeling chemistry, physics, economy and engineering problems. In this paper, a new iterative approach for finding a solution of a nonlinear equations system (NLES) is presented by applying a linearization technique. The proposed approach is based on computational method that converts NLES into a linear equations system by using Taylor series expansion at the chosen arbitrary nonnegative initial point. Using the obtained solution of the linear equations system, a linear programming (LP) problem is constructed by considering the equations as constraints and minimizing the objective function constructed as the summation of balancing variables. At the end of the presented algorithm, the exact solution of the NLES is obtained. The performance of the proposed approach has been demonstrated by considering different numerical examples from literature.