Optimization
Stochastic optimization procedures try to provide solutions to optimization problems which have many local minima in their objective function. For these optimization problems the usual steepest descent algorithms fail as they get easily caught in local minima. For such problems stochastic optimization procedures and especially simulated annealing have been used with growing success -- not to determine the global minimum but to provide "good" solutions with values of the objective which are not too "far" apart from the desired global minimum. Simulated annealing is based on the idea of a controlled thermal relaxation dynamic in the state of the system, where the objective function to be minimized is the energy. Not surprisingly, it turns out that the concept of an energy landscape is particularly helpful in describing the thermal relaxation dynamics which leads to a solution of the underlying optimization problem. We investigate the controlled optimization dynamics on energy landscapes using tools from mathematics and from theoretical physics. Typical methods employed are the theory of Markov processes as well as simulation techniques.