Oscillatory Descent for Function Minimization

Algorithms for minimizing a function based on continuous descent methods following the gradient relative to some riemannian metric suffer from the twin problems of converging to local, rather than global, minima and giving little indication about an approximate answer until the process has nearly converged. Simulated annealing addresses these problems through the introduction of stochastic terms, however the rate of convergence associated with the method can be unacceptably slow. In this paper we discuss a modification of simulated annealing which approaches a minimum through a damped oscillatory path. The characteristics of the path, including its tendency to be irregular, reflect the properties of the function being minimized. The oscillatory algorithm involves both a temperature and coupling parameters, giving it considerable flexibility.