Neural Network to solve optimization problems

I am very new to neural network. I know that after training, we can obtained a network which we can get the output with the related inputs. My question is: can we use neural network to solve optimization problems without training data. For example, I have 2 inputs and 2 outputs network and outputs are used to calculate in another function in the purpose of minimizing that function. Can neural network be used in problem like this? and if it is possible, what kind of neural network we can use? And what command in Matlab can we use? Thank you very much in advance.

[awezmm]

There are trained are trained networks out there if you don't have any training data.