Abstract: Firstly, the author gave properties of three uniform smooth approximation functions for absolute value function from above, and demonstrated their approximation effect with images. Secondly, a new method for solving linear programming problems was given. First, the linear programming problem was transformed into nonlinear equations, then the smooth 
nonlinear equations were obtained by uniform smooth approximation function, and then solved by high order Newton method. Numerical experiments show that approximation degree of uniform smooth function from above adopted in this method is superior to the existing algorithms, and the computational time is less under the same conditions.

Key words: linear programming, high order Newton method, uniform smooth approximation function from above, absolute value function, nonlinear equations