## Initial Points for Global Optimization Toolbox Solvers

Some Global Optimization Toolbox solvers require an initial point `x0`: `patternsearch`, `simulannealbnd`, `GlobalSearch`, and `MultiStart`. When solving optimization problems using the problem-based approach, you specify `x0` in the second argument for `solve` and for `prob2struct`. To specify an initial point, create a structure with the variable names as fields and variable values as structure values. For example, for a scalar variable `x` and a 2-by-2 matrix `y` for the `patternsearch` solver, enter the following code.

```x0.x = 5; x0.y = eye(2) + 0.1*randn(2); [sol,fval] = solve(prob,x0,"Solver","patternsearch")```

You can also specify an initial point for these solvers using `optimvalues`, as shown next.

Other Global Optimization Toolbox solvers do not require an initial point, but can accept an initial point or set of initial points: `ga`, `gamultiobj`, `paretosearch`, and `surrogateopt`. To pass initial points to these solvers, create the points using `optimvalues`.

Note

When using the problem-based approach, you cannot pass an initial point or initial population using options such as:

For example, take a 2-D variable `x` and a 2-by-2 matrix `y` for the `ga` solver.

```x = optimvar('x',2,"LowerBound",-1,"UpperBound",1); y = optimvar('y',2,2,"LowerBound",-1,"UpperBound",1); prob = optimproblem("Objective",... cosh(dot(y*x,[2;-1])) - sinh(dot(y*x,[1;-2]))); prob.Constraints = y(1,2) == y(2,1); % Set initial population: x0x for x, x0y for y rng default x0x = [1;1/2]; x0y = eye(2)/2 + 0.1*randn(2); x0 = optimvalues(prob,'x',x0x,'y',x0y); % Solve problem [sol,fval] = solve(prob,Solver="ga")```
```ga stopped because the average change in the fitness value is less than options.FunctionTolerance. sol = struct with fields: x: [2×1 double] y: [2×2 double] fval = -48.6317```

The solution satisfies the constraint `y(1,2) == y(2,1)` only to within the constraint tolerance `1e-3`: `sol.y(2,1) = -1.0000`, but `sol.y(1,2) = -0.9990`.