However, due to the existence of multiple local minimiz-ers that differ from the global solution, we have to face two difficulties: how to jump from a local minimizer to a smaller one and how to judge that the current minimizer is a global one.

A novel global optimization training algorithm was constructed for the feed-forward neural networks to which the BP algorithm is easy to fall into the local minimum point for improper choice of initial weights.

The training process of Back Propagation Neural Network (BPNN) is easily converged at a local minimum, which slows the training process sharply.

The advantages of applying simulated annealing algorithm to short-term load forecast include less model complexity,high forecasting accuracy and global optimal property,which alleviate the tendency of traditional BP algorithm to be trapped in local minimum.

Then some defects such as slow convergence rate and getting into local minimum in BP algorithm are pointed out,and the root of the defects is presented.

With the purpose of solving the local minima of standard Back-Propagation(BP) algorithm,a modified error function was proposed to escape from the local minima and converge to the global minima.

Homotopy method for getting a local minimum of unconstrained non-convex programming

It is emphazised that the local minimum problem caused by null resultant force or U shape obstacle is studied.

In this paper, we study several models of Hopfield neural network to overcome the difficulties of the invalid solution and local minimum in solving the Travelling Saleman Problem(TSP).