I am using the Trust Region Method (Nocedal & Wright, 2006) for optimization problems and the search of minima starting from a saddle point, I have created an algorithm and it works very well, however I have the following problem, for example in the following graph I show the Muller-Brown functional (Muller & Brown, 1979), where it can be observed that the optimization starts from a saddle point and reaches the minimum at C, my doubt is the following, what mathematical method or modification could I make to the optimization method so that at the moment of optimizing instead of going to point C (nature of the algorithm) it would be to point A (which is already known), I would force the algorithm to go to point A at the moment of optimizing.
I would be grateful for any recommended bibliography that deals with this problem of mathematical nature to replicate it in my case in a computer algorithm.
References:
- Jorge Nocedal & Stephen J Wright, 2006. Numerical Optimization, second edition.
- Muller & Brown, 1979. Location of Saddle Points and Minimum Energy Paths by a Constrained Simplex Optimization Procedure. Theoret. Chim. Acta (Berl.) 53, 75-93.