Create Problem Structure

About Problem Structures

To use the GlobalSearch or MultiStart solvers, you must first create a problem structure. There are two recommended ways to create a problem structure: using the createOptimProblem function and exporting from the Optimization app.

Using 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,eflag,output] = fmincon(problem);
```

Example: Creating 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.

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,eflag,output] = fmincon(problem);
```

Exporting from the Optimization app

Follow these steps to create a problem structure using the Optimization app.

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 nonlinear constraint functions. For details, see Nonlinear Constraints.
Create a start point. For example, to create a three-dimensional random start point xstart:
```
xstart = randn(3,1);
```
Open the Optimization app by entering optimtool at the command line, or by choosing the Optimization app from the Apps tab.
Choose the local Solver.
- For GlobalSearch: fmincon (default).
- For MultiStart:
  - fmincon (default)
  - fminunc
  - lsqcurvefit
  - lsqnonlin
  For help choosing, see Optimization Decision Table.
Choose an appropriate Algorithm. For help choosing, see Choosing the Algorithm.
Set an initial point (Start point).
Include the function handle for your objective function in Objective function, and, if applicable, include your Nonlinear constraint function. For example,
Set bounds, linear constraints, or local Options. For details on constraints, see Write Constraints.
Best practice: run the problem to verify the setup.
Choose File > Export to Workspace and select Export problem and options to a MATLAB structure named

Example: Creating a Problem Structure with the Optimization App

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.

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;
```
Launch the Optimization app by entering optimtool at the MATLAB^® command line.
Set the solver, algorithm, objective, start point, and constraints.
Best practice: run the problem to verify the setup.
The problem runs successfully.
Choose File > Export to Workspace and select Export problem and options to a MATLAB structure named

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