Optimization of two linear models with constraint

I have a dataset which is a 'v-shaped' pattern of dots: y_observed and want to adjust two linear regressions with a turning point TP so that a cost function minimices the errors for the to models, y_calc1=m1*x(1:TP)+b1, y_calc2=m2*x(TP:end)+b2 AND y_calc1(TP)=y_calc2(TP).

Can somebody help me with this? its a simple 'fmincon' problem

Answer 1

[Matt J]

This should be applicable.

http://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation

What you describe is a first order spline with a single free knot.

[Mario Trevino]

Fantastic! thank you very much