curve fitting with trend

Hi,

I want to fit a curve in matlab by giving a initial guess and i want the curve fitting algorithm to maintain the same trend as my initial guess, even if the coefficient doesn't fully fits the curve also it is fine. Does least square method does this?

For example,

My initial guess is [10,12,17,21] i want the output in the same trend(in this case it is increasing), say i need an output like [1,2,3.5,5] or may be [100,104,107,110] but not like [1,-40,200,5]. Does any function does this?

My second question,

if i want to fit a curve in matlab i want to create a function and then feed the initial guess but what if my function has an intrepolation function in it? Will the system still solves(i'm aware that nlinfit will solve it but not follows the trend of initial guess)?

I've both optimization and curve fitting toolbox.