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Conjugate gradient backpropagation with Powell-Beale restarts

`net.trainFcn = 'traincgb'`

[net,tr] = train(net,...)

`traincgb`

is a network training function that
updates weight and bias values according to the conjugate gradient
backpropagation with Powell-Beale restarts.

`net.trainFcn = 'traincgb'`

sets the network `trainFcn`

property.

`[net,tr] = train(net,...)`

trains the network
with `traincgb`

.

Training occurs according to `traincgb`

training
parameters, shown here with their default values:

`net.trainParam.epochs` | `1000` | Maximum number of epochs to train |

`net.trainParam.show` | `25` | Epochs between displays ( |

`net.trainParam.showCommandLine` | `false` | Generate command-line output |

`net.trainParam.showWindow` | `true` | Show training GUI |

`net.trainParam.goal` | `0` | Performance goal |

`net.trainParam.time` | `inf` | Maximum time to train in seconds |

`net.trainParam.min_grad` | `1e-10` | Minimum performance gradient |

`net.trainParam.max_fail` | `6` | Maximum validation failures |

`net.trainParam.searchFcn` | `'srchcha'` | Name of line search routine to use |

Parameters related to line search methods (not all used for all methods):

`net.trainParam.scal_tol` | `20` | Divide into |

`net.trainParam.alpha` | `0.001` | Scale factor that determines sufficient reduction in |

`net.trainParam.beta` | `0.1` | Scale factor that determines sufficiently large step size |

`net.trainParam.delta` | `0.01` | Initial step size in interval location step |

`net.trainParam.gama` | `0.1` | Parameter to avoid small reductions in performance, usually
set to |

`net.trainParam.low_lim` | `0.1` | Lower limit on change in step size |

`net.trainParam.up_lim` | ` 0.5` | Upper limit on change in step size |

`net.trainParam.maxstep` | `100` | Maximum step length |

`net.trainParam.minstep` | `1.0e-6` | Minimum step length |

`net.trainParam.bmax` | `26` | Maximum step size |

You can create a standard network that uses `traincgb`

with `feedforwardnet`

or `cascadeforwardnet`

.

To prepare a custom network to be trained with `traincgb`

,

Set

`net.trainFcn`

to`'traincgb'`

. This sets`net.trainParam`

to`traincgb`

's default parameters.Set

`net.trainParam`

properties to desired values.

In either case, calling `train`

with the resulting
network trains the network with `traincgb`

.

`traincgb`

can train any network as long as
its weight, net input, and transfer functions have derivative functions.

Backpropagation is used to calculate derivatives of performance `perf`

with
respect to the weight and bias variables `X`

. Each
variable is adjusted according to the following:

X = X + a*dX;

where `dX`

is the search direction. The parameter `a`

is
selected to minimize the performance along the search direction. The
line search function `searchFcn`

is used to locate
the minimum point. The first search direction is the negative of the
gradient of performance. In succeeding iterations the search direction
is computed from the new gradient and the previous search direction
according to the formula

dX = -gX + dX_old*Z;

where `gX`

is the gradient. The parameter `Z`

can
be computed in several different ways. The Powell-Beale variation
of conjugate gradient is distinguished by two features. First, the
algorithm uses a test to determine when to reset the search direction
to the negative of the gradient. Second, the search direction is computed
from the negative gradient, the previous search direction, and the
last search direction before the previous reset. See Powell, *Mathematical
Programming,* Vol. 12, 1977, pp. 241 to 254, for a more
detailed discussion of the algorithm.

Training stops when any of these conditions occurs:

The maximum number of

`epochs`

(repetitions) is reached.The maximum amount of

`time`

is exceeded.Performance is minimized to the

`goal`

.The performance gradient falls below

`min_grad`

.Validation performance has increased more than

`max_fail`

times since the last time it decreased (when using validation).

Powell, M.J.D., "Restart procedures for the conjugate
gradient method," *Mathematical Programming*,
Vol. 12, 1977, pp. 241–254

`trainbfg`

| `traincgf`

| `traincgp`

| `traingda`

| `traingdm`

| `traingdx`

| `trainlm`

| `trainoss`

| `trainscg`

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