How can I express sum of an optimvar raised to a power

I am getting an error saying [Undefined operator '^' for input arguments of type 'optim.problemdef.OptimizationVariable'.] when I write the following code:

x = optimvar('x');
syms d;
z = symsum(x^d,d,1,5);

can anybody tell me how to code it correctly

Answer 1

[Alan Weiss]

There are several problems with what you are trying to do. As the documentation explicitly states, the only supported operations on optimization variables are linear or quadratic ( x.^2 or x.*y sort of things). And quadratic was added in R2018b, which just came out, so unless you have the very latest software, you can use only linear expressions with optimization variables. In addition, you are attempting to mix symbolic math with optimization variables, and those two things are objects of different classes, and do not interoperate.

I'm glad that you like optimization variables, but currently their use is restricted to linear or quadratic problems.

Alan Weiss

MATLAB mathematical toolbox documentation

[Jijo Varghese]

Thank you for the info. But can you suggest an alternative instead of using optimvar for declaring optimization variables. I want to perform double summation for set limits and summation-product sum operations. How can I do these operations without using the sym function.

[Matt J]

You can do all of that non-symbolically, e.g.,

t=(1:5);

tsum=sum(t.^3),

Moreover, since you have a non-linear optimization problem, you are going to need to implement this way because the non-linear solvers in the Optimization Toolbox are all numeric (not symbolic) solvers.

[Walter Roberson]

The Symbolic Toolbox can be useful in creating formulae to be optimized.

In some cases it can be effective to do optimization symbolically, by differentiating and solving the result for 0.

In other cases, after generating the formula, you would use matlabFunction() to create an anonymous function that can evaluate a given position numerically.

Equation fitting can, in general, be handled by constructing the function f based upon symbolic vector x and symbolic parameters to be searched for, and then doing

OBJ = sum( (subs(f, x, KNOWN_X) - KNOWN_Y).^2 );

and then using matlabFunction() on OBJ, specifying the parameters with the 'vars' option using the {[Variables]} form. For example,

obj = matlabFunction(OBJ, 'vars', {[a, b, p]})

for an equation with parameters a, b, and p.

The resulting obj function will calculate the sum-of-squares residue for a row vector of coefficients, which you would then attempt to minimize. You would probably not use just plain fmincon for this purpose, as fmincon easily gets stuck in local minima, but you might use a global optimization technique, including potentially just multistart of fmincon (that is, evaluate at a number of different starting points.)