Objective function of traditional Support Vector Machine is a strictly convex quadratic problem

but is not differentiable due to plus function

which precludes the most used optimization algorithms.For support vector regression model

this paper presents tangent circular arc smooth function to approximate plus function in original un-differentiable model

and makes the objective function of traditional support vector regression machine smooth.Properties of tangent circular arc smooth function are analyzed

convergence of tangent circular arc smooth support vector regression model is proved

and how to determine the smallest value of smoothness factor α when meets the requirement of the preset precision is given.