My solution was to put all these equations into one long one:
It's tempting to write your expression as one big anonymous function, but in this case with a somewhat complicated equation I'd recommend writing up your objective function as a normal function instead. Doing so will have a few benefits:
- You can define intermediate terms using good, descriptive names. When someone else reads your code (or when you read it six months from now) the hints about the purpose of those variables given by the names could prove very useful in understanding what the code is doing. As it stands right now your problem statement has a number of variables defined that don't appear in your objective function; where do c, k1, and k2 get used in your function fun?
- Related to the first point, you can add comments indicating the purpose of each step. This doesn't necessarily mean explaining what the code is doing (ideally that should be obvious from what functions you're calling) but more importantly means explaining why the code does what it does. Something like "We tried using approach X here but need to use approach Y instead to avoid catastrophic cancellation" is an example of a good why comment IMO.
- You can step through the code in the debugger. If you have an example of evaluating your function by hand that you've worked out step-by-step, you can step through the code with the debugger line-by-line and confirm that each step is doing what you expect it to do.
Your format for your nonlinear constraint function is incorrect. If you look at the description of the nonlcon input on the fmincon documentation page, you'll see that it states " nonlcon is a function that accepts a vector or array x and returns two arrays, c(x) and ceq(x)." There are two problems here.
chi = fmincon(fun, x0,A,b,Aeq,beq,lb,ub,nonlcon)
function [c,ceq] = nonlcon(x,lambda_1,lambda_2)
The first is that when you call fmincon you're calling nonlcon with 0 input arguments and passing whatever that function call returns as the nonlcon input argument. That won't work. Specify it as a function handle instead, @nonlcon.
The second is that your nonlcon function accepts three inputs (and requires all three to work), not one as the documentation states. If lambda_1 and lambda_2 are additional constant parameters you want to pass into nonlcon you can do that using one of the techniques shown on this documentation page.
