Energy Minimization
I am doing undergraduate research in a lab that does molecular dynamics simulations and it struck me yesterday that the minimization of energy functions could be done with the methods I learned in vector calculus if one was to apply constraints to a system of equations with 3N variables, where N is the number of atoms.I went through a book on molecular modeling yesterday to see if it said anything regarding this and it stated that it is not generally possible to do that "for molecular systems due to the complicated way in which the energy varies with the coordinates." It then states that minimization is done with numerical methods, but it does not elaborate on why the way that the energy is modeled prevents use of the extreme value theorem.
Would someone elaborate on the nature of problems where the extreme value theorem cannot be used for minimization of a system of variables?
If I do not get a response here, I will ask in the lab on Monday, but people here seem to be really good at applied mathematics, so I was hoping that someone here could elaborate on what the book said.
