# Documentation

## Create Problem Structure

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

For information on creating inputs for the problem structure, see Inputs for Problem Structure.

### Using the createOptimProblem Function

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

1. 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.

2. If relevant, create your constraints, such as bounds and nonlinear constraint functions. For details, see Write Constraints.

3. Create a start point. For example, to create a three-dimensional random start point `xstart`:

`xstart = randn(3,1);`
4. (Optional) Create an options structure using `optimoptions`. For example,

`options = optimoptions(@fmincon,'Algorithm','interior-point');`
5. 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.

6. 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,`
7. Include the function handle for your objective function in `objective`:

```problem = createOptimProblem('fmincon','x0',xstart, ... 'objective',@objfun,```
8. Set bounds and other constraints as applicable.

ConstraintName
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'`

9. If using the `lsqcurvefit` local solver, include vectors of input data and response data, named `'xdata'` and `'ydata'` respectively.

10. 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]`.

1. 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);```
2. Write the linear constraint matrices. Change the constraint to "less than" form:

```A = [-1,-2]; b = -4;```
3. Create the local options structure to use the `interior-point` algorithm:

`opts = optimoptions(@fmincon,'Algorithm','interior-point');`
4. Create the problem structure with `createOptimProblem`:

```problem = createOptimProblem('fmincon', ... 'x0',[2;3],'objective',sixmin, ... 'Aineq',A,'bineq',b,'options',opts)```
5. The resulting structure:

```problem = 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]```
6. 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.

1. 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.

2. If relevant, create nonlinear constraint functions. For details, see Nonlinear Constraints .

3. Create a start point. For example, to create a three-dimensional random start point `xstart`:

`xstart = randn(3,1);`
4. Open the Optimization app by entering `optimtool` at the command line, or by choosing the Optimization app from the Apps tab.

5. Choose the local Solver.

• For `GlobalSearch`: `fmincon` (default).

• For `MultiStart`:

• `fmincon` (default)

• `fminunc`

• `lsqcurvefit`

• `lsqnonlin`

For help choosing, see Optimization Decision Table.

6. Choose an appropriate Algorithm. For help choosing, see Choosing the Algorithm.

7. Set an initial point (Start point).

8. Include the function handle for your objective function in Objective function, and, if applicable, include your Nonlinear constraint function. For example,

9. Set bounds, linear constraints, or local Options. For details on constraints, see Writing Constraints.

10. Best practice: run the problem to verify the setup.

11. 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]`.

1. 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);```
2. Write the linear constraint matrices. Change the constraint to "less than" form:

```A = [-1,-2]; b = -4;```
3. Launch the Optimization app by entering `optimtool` at the MATLAB® command line.

4. Set the solver, algorithm, objective, start point, and constraints.

5. Best practice: run the problem to verify the setup.

The problem runs successfully.

6. Choose File > Export to Workspace and select Export problem and options to a MATLAB structure named