Optimization of objective function with integrals where a bound is an optimization variable

I am attempting to maximize an objective function with integrals where the integrals' upper bounds are also the choice variables. e.g. I would like to maximize the following by choice of a 10x1 vector v

[int_0^v(1) (a(1)/(v(1))^(e(1)) dv(1) - b(1)*v(1)] + [int_0^v(2) (a(2)/(v(2))^(e(2)) dv(2) - b(2)*v(2)] + ... + [int_0^v(10) (a(10)/(v(10))^(e(10)) dv(10) - b(10)*v(10)]

My code is:

n=10;
a=rand(n,1);
b=rand(n,1)*3;
e=rand(n,1)*(-1);

prob= optimproblem('ObjectiveSense','max');
v=optimvar('v',n,1,'LowerBound',0);
series=int((a./v).^(e),0,v) -b.*v;
expand=sum(series);
prob.Objective=expand;
showproblem(prob)
sol=solve(prob);
sol.v

I receive the error "optim.internal.problemdef.Rdivide.getRdivideOperator Division by an OptimizationVariable not supported."

However, I also don't believe that I can use the 'int' function form optimization variables either, so I may be going about the problem entirely incorrectly.

[Torsten]

0 < e(i) < 1 for 1 <= i <= 10 ?

[CN_218]

Yes

[Torsten]

Then v(i) = a(i)/b(i)^(1/e(i)) for 1 <= i <= 10.

Answer 1

[Alan Weiss]

Currently, the problem-based approach, using optimproblem and the like, is only for linear or quadratic objective functions with linear constraints. To use Optimization Toolbox™ solvers, you will have to formulate your problem using the solver-based approach.

Alan Weiss

MATLAB mathematical toolbox documentation