There is a single minimum. In nonlinear networks, however, the cost surface can be very complex. There can be many minima, valleys, plateau's which make training very difficult. Batch gradient descent will simply move the bottom of the local minimum it randomly starts in. If it is on a plateau, the gradient may be very small and so learning takes a very long time.
Valleys are common when using sigmoids.
Consider what happens when sigmoids are added. Below, the green sigmoid is added to the blue to obtain the red. Now, look what can happen in 2 dimensions. It can help somewhat with valleys as well. The bad news is that this added flexibility can cause the network to learn the noise in the data.