Curve fitting (line of best fit) from a set of inequalities

I want a custom-made computer applet (windows compatible) to approximate a curve. This is a curve-fitting problem, like you get in SPSS or other statistics programs, but instead of coordinate points we have a set of inequalities: Imagine you have a bounded function f defined on a closed interval, say [0, 10] (I want the program to allow me to set this interval), which is increasing throughout the domain, f’x ≥0. It’s a simple polynomial function (up to 3rd degree). The only information you are given is a set of inequalities of the following form (note that sometimes the left and sometimes the right hand side is larger): f(xi1)> f(xj1) + f(xk1) f(xi2)< f(xj2) + f(xk2) f(xi3)> f(xj3) + f(xk3). . . . . . . . f(xin)> f(xjn) + f(xkn) where the xi on the left hand side of the equation is always larger than both the xj and xk on the right hand side (because we know that the function is increasing). I would like a program that would allow me to insert the values into the set of inequalities (as many inequalities as I want, but realistically I wouldn’t need more than 30) and give me the best-fitting function, i.e. the function that correctly predicts the largest number of inequalities. I would also like the program to give me the percentage of correctly predicted inequalities, and highlight (in red maybe) the inequalities that don’t fit this best-fitting function. I have no programming knowledge, so this would need to be intuitive, where I just point and click and enter values.