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Parallel Optimization Functionality |

Parallel computing is the technique of using multiple processors on a single problem. The reason to use parallel computing is to speed computations.

The Optimization Toolbox™ solvers `fmincon`, `fgoalattain`,
and `fminimax` can automatically distribute the
numerical estimation of gradients of objective functions and nonlinear
constraint functions to multiple processors. These solvers use parallel
gradient estimation under the following conditions:

You have a license for Parallel Computing Toolbox™ software.

The option

`GradObj`is set to`'off'`, or, if there is a nonlinear constraint function, the option`GradConstr`is set to`'off'`. Since`'off'`is the default value of these options, you don't have to set them; just don't set them both to`'on'`.Parallel computing is enabled with

`parpool`, a Parallel Computing Toolbox function.The option

`UseParallel`is set to`true`. The default value of this option is`false`.

When these conditions hold, the solvers compute estimated gradients in parallel.

One subroutine was made parallel in the functions `fmincon`, `fgoalattain`,
and `fminimax`: the subroutine that estimates the
gradient of the objective function and constraint functions. This
calculation involves computing function values at points near the
current location *x*. Essentially, the calculation
is

where

*f*represents objective or constraint functions*e*are the unit direction vectors_{i}Δ

_{i}is the size of a step in the*e*direction_{i}

To estimate ∇*f*(*x*) in
parallel, Optimization Toolbox solvers distribute the evaluation
of (*f*(*x* + Δ_{i}*e*_{i})
– *f*(*x*))/Δ_{i} to
extra processors.

You can choose to have gradients estimated by central finite differences instead of the default forward finite differences. The basic central finite difference formula is

This takes twice as many function evaluations as forward finite differences, but is usually much more accurate. Central finite differences work in parallel exactly the same as forward finite differences.

Enable central finite differences by using `optimoptions` to
set the `FinDiffType` option to `'central'`.
To use forward finite differences, set the `FinDiffType` option
to `'forward'`.

Solvers employ the Parallel Computing Toolbox function `parfor` to perform parallel estimation
of gradients. `parfor` does not work in parallel
when called from within another `parfor` loop.
Therefore, you cannot simultaneously use parallel gradient estimation
and parallel functionality within your objective or constraint functions.

Suppose, for example, your objective function `userfcn` calls `parfor`,
and you wish to call `fmincon` in a loop. Suppose
also that the conditions for parallel gradient evaluation of `fmincon`,
as given in Parallel Optimization Functionality, are satisfied. When parfor Runs In Parallel shows three
cases:

The outermost loop is

`parfor`. Only that loop runs in parallel.The outermost

`parfor`loop is in`fmincon`. Only`fmincon`runs in parallel.The outermost

`parfor`loop is in`userfcn`.`userfcn`can use`parfor`in parallel.

**When parfor Runs In Parallel**

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