How to pass a linear dependence between some parameters into MATLAB non linear solver?

I am fitting a multiparametric model based on a set of differential equations to the experimental data.

I have initial guesses:

par0=  [  1.0,    0.05,    1.0,   0.01,    2*12*1000,   100*4,   300,  2.25,   0,           0.35, 0.43, 0.54, 0.67, 0.8, 0.94]; 
     lb...
     ub...
problem=createOptimProblem('lsqcurvefit','objective',@doFit,'x0',par0,'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata');
ms = MultiStart('TolFun',1e-20,'TolX',1e-20);
par= run(ms,problem,10);

I know that there is a linear dependence between par(10),par(11),par(12),par(13),par(14),par(15), par(16) like sketched in the plot

How to pass this dependence into the solver? Thank you in advance.

Answer 1

[Matt J]

Are you saying par(10:16) lies on a line of known slope? If so, you can eliminate par(11:16) from the problem using the equation

 par(11:16)=par(10)+slope*(1:6)

Using the above equation, everything can be written in terms of par(1:10) only.