how to define sqrt in Optimization?

HI,

I would like to implemet sqrt and round functions in optimization. Can anyone help me how to do that?

objoptim=clOptimization;
w=opt(objoptim);

classdef clOptimization
    properties
        P=optimvar('P',2)
    end
    methods
        function w=opt(obj)
            y=obj.P(1);
            z=sqrt(y*obj.P(2));
            w=round(y*z);
        end
    end
end

This is just an example to know the syntax. Can anyone help me.

Answer 1

[Alan Weiss]

I'm not sure what you are talking about. If you are trying to extend the problem-based method, then the short answer is you are on your own, there is no documented way to extend the problem-based functions. If you are talking about something else, then please describe what you are trying to do in more detail.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Walter Roberson]

sqrt() is already defined for optimization expressions, at least in R2020a.

https://www.mathworks.com/matlabcentral/answers/580371-error-using-conversion-to-optim-problemdef-optimizationexpression-from-optim-problemdef-optimiz#comment_975147

>> A = optimvar('A')

A = 

  OptimizationVariable with properties:

          Name: 'A'
          Type: 'continuous'
    IndexNames: {{}  {}}
    LowerBound: -Inf
    UpperBound: Inf

  See variables with show.
  See bounds with showbounds.

>> sqrt(A)

ans = 

  Nonlinear OptimizationExpression

    sqrt(A)

Be careful though, as sqrt() is not differentiable at 0.

I do not currently see any way to achieve round() using the supported functions.

round() is not differentiable at integers (and has a derivative of 0 at real values that are not integers).

Remember that the underlying optimization algorithms assume differentiability for any variable not marked as integer.

The supported integer constraints involve using intlinprog() solver, which does not support non-linear objectives -- the objective must be resolvable to a matrix multiplication, not to a generalized function.

If you need a generalized function as the objective, then you cannot turn it into an effectively integer-constraint problem by using round(): the optimization functions will fail badly on it, thinking that the objective function is flat near the integer locations.

If you need non-linear functions plus integer constraints, then you should be using ga() or gamultiobj() or paretosearch()