I wrote an article titled “Understanding Neural Network Batch Training: A Tutorial” in the August 2014 issue of Visual Studio Magazine. See http://visualstudiomagazine.com/articles/2014/08/01/batch-training.aspx.
By far the most common technique used to train a neural network is called back-propagation. But there are alternatives including using particle swarm optimization, or using simplex optimization. Each of the possible training techniques can be applied using one of two approaches, usually called “batch” and “online” training.
In batch training, in each iteration of the main training loop, all training data items are examined and their associated errors (differences between the computed output values and the actual output values) are then used to modify the network’s weights and bias values.
In online training, in each iteration of the main training loop, after each test item is fed to the network, weights and bias values are immediately updated.
Research suggest that online training is quite a bit superior to batch training when using back-propagation, but research results are not clear if online training is better when using particle swarm or simplex optimization.