Create Problem Structure

About Problem Structures

To use the GlobalSearch or MultiStart solvers, you must first create a problem structure. The recommended way to create a problem structure is using the createOptimProblem function. You can create a structure manually, but doing so is error-prone.

Use the `createOptimProblem` Function

Follow these steps to create a problem structure using the createOptimProblem function.

Define your objective function as a file or anonymous function. For details, see Compute Objective Functions. If your solver is lsqcurvefit or lsqnonlin, ensure the objective function returns a vector, not scalar.
If relevant, create your constraints, such as bounds and nonlinear constraint functions. For details, see Write Constraints.
Create a start point. For example, to create a three-dimensional random start point xstart:
```
xstart = randn(3,1);
```
(Optional) Create options using optimoptions. For example,
```
options = optimoptions(@fmincon,'Algorithm','interior-point');
```
Enter
```
problem = createOptimProblem(solver,
```
where solver is the name of your local solver:
- For GlobalSearch: 'fmincon'
- For MultiStart the choices are:
  - 'fmincon'
  - 'fminunc'
  - 'lsqcurvefit'
  - 'lsqnonlin'
  For help choosing, see Optimization Decision Table.
Set an initial point using the 'x0' parameter. If your initial point is xstart, and your solver is fmincon, your entry is now
```
problem = createOptimProblem('fmincon','x0',xstart,
```

Include the function handle for your objective function in objective:

problem = createOptimProblem('fmincon','x0',xstart, ...
    'objective',@objfun,

Set bounds and other constraints as applicable.

Constraint	Name
lower bounds	`'lb'`
upper bounds	`'ub'`
matrix `Aineq` for linear inequalities `Aineq x` ≤ `bineq`	`'Aineq'`
vector `bineq` for linear inequalities `Aineq x` ≤ `bineq`	`'bineq'`
matrix `Aeq` for linear equalities `Aeq x` = `beq`	`'Aeq'`
vector `beq` for linear equalities `Aeq x` = `beq`	`'beq'`
nonlinear constraint function	`'nonlcon'`

If using the lsqcurvefit local solver, include vectors of input data and response data, named 'xdata' and 'ydata' respectively.
Best practice: validate the problem structure by running your solver on the structure. For example, if your local solver is fmincon:
```
[x,fval,exitflag,output] = fmincon(problem);
```

Example: Create a Problem Structure with `createOptimProblem`

This example minimizes the function from Run the Solver, subject to the constraint x₁ + 2x₂ ≥ 4. The objective is

sixmin = 4x² – 2.1x⁴ + x⁶/3 + xy – 4y² + 4y⁴.

(1)

Use the interior-point algorithm of fmincon, and set the start point to [2;3].

Write a function handle for the objective function.

sixmin = @(x)(4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ...
    + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4);

Write the linear constraint matrices. Change the constraint to “less than” form:
```
A = [-1,-2];
b = -4;
```

Create the local options to use the interior-point algorithm:

opts = optimoptions(@fmincon,'Algorithm','interior-point');

Create the problem structure with createOptimProblem:

problem = createOptimProblem('fmincon', ...
    'x0',[2;3],'objective',sixmin, ...
    'Aineq',A,'bineq',b,'options',opts)

The resulting structure:

problem = 

  struct with fields:

    objective: @(x)(4*x(1)^2-2.1*x(1)^4+x(1)^6/3+x(1)*x(2)-4*x(2)^2+4*x(2)^4)
           x0: [2x1 double]
        Aineq: [-1 -2]
        bineq: -4
          Aeq: []
          beq: []
           lb: []
           ub: []
      nonlcon: []
       solver: 'fmincon'
      options: [1x1 optim.options.Fmincon]

Best practice: validate the problem structure by running your solver on the structure:
```
[x,fval,exitflag,output] = fmincon(problem);
```