varindex

Create an optimization problem.

x = optimvar('x',3);
y = optimvar('y',3,3);
prob = optimproblem('Objective',x'*y*x);

Convert the problem to a structure.

problem = prob2struct(prob);

Obtain the linear indices in problem of all prob variables.

idx = varindex(prob);
disp(idx.x)

     1     2     3

disp(idx.y)

     4     5     6     7     8     9    10    11    12

Obtain the y indices only.

idxy = varindex(prob,'y')

idxy = 1×9

     4     5     6     7     8     9    10    11    12

This example shows how to obtain most of the same information using either the problem-based approach or the solver-based approach. First create a problem and solve it using the problem based approach.

x = optimvar('x',3,1,'LowerBound',1,'UpperBound',1);
y = optimvar('y',3,3,'LowerBound',-1,'UpperBound',1);
prob = optimproblem('Objective',x'*y*x + [2 3 4]*x);
rng default
x0.x = rand(3, 1);
x0.y = rand(3, 3);
[solp,fvalp,exitflagp,outputp] = solve(prob,x0);

Solving problem using fmincon.

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

Next, convert the problem to solver-based form using prob2struct. To have the fmincon solver use the automatic gradients in the problem, set the SpecifyObjectiveGradient option to true.

solverprob = prob2struct(prob,x0);
solverprob.options = optimoptions(solverprob.options,"SpecifyObjectiveGradient",true);

Solve the problem using fmincon.

[sols,fvals,exitflags,outputs] = fmincon(solverprob);

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

To convert the fmincon solution to the structure form returned by solve, create appropriate structures using varindex.

idx = varindex(prob);
sol.x = sols(idx.x);
sol.y = sols(idx.y);

The y index that varindex uses is a linear index. Reshape the variable sol.y to have the size of x0.y.

sol.y = reshape(sol.y,size(x0.y));

Check that the two solution structures are identical.

isequal(sol,solp)

ans = logical
   1

The reason that the two approaches are not completely equivalent is that fmincon can return more arguments such as Lagrange multipliers, whereas solve cannot.