I want to implement u_c = argmin ( u_nom - u)^2 subject to \dot(h) + \alpha * h geq 0

let me know how to use argmin subject to an inequality constraint

[John D'Errico]

We need to read your mind.

Let me see. You want to minmize the square of the difference between u, and u_nom, subject to an inequality constraint on some variables that seem not to be related to u at all? And possibly (we don't know this), but possibly, the inequality constraint MAY be a differential equation? That is, is the variable hdot actually the time derivative of h? Or something like that?

Is u a scalar? u_nom? How does it relate to alpha? h? hdot?

Sorry. I'm trying to read your mind as to what you actually mean by that vaguely specified problem, but the MATLAB crystal ball is so foggy today.

Seriously, how would you write that? That is impossible to know. This might be a differential equation problem. It might be an optimization problem, so possibly you would need to use fmincon or GA. But beyond that, you need to be far more clear about the question.

[Pallov Anand]

Thanks for your comment....actually i was looking for some function like "argmin" if it exists in matlab or not....but i guess i can do this using "fmincon".

Thanks for your time and detailed comment :)

[Walter Roberson]

There are several different minimization routines in MATLAB, none of which happen to be called "argmin" . But also, none of the built-in routines in the Optimization Toolbox or the Global Optimization Toolbox happen to handle differential equations or integral equations.

[Torsten]

@Pallov Anand

https://en.wikipedia.org/wiki/Arg_max

"argmin" means a point x0 where a function f is minimal: f(x0) <= f(x) for all feasible points x.

To see how MATLAB can be used to solve optimal control problems like yours, take a look at

https://www.youtube.com/watch?v=60xX4R708Iw