Stochastic minimization with adaptive memory

In this paper a nondeterministic minimization algorithm is presented. A common feature of random search algorithms is that little or no use is made of information on the local structure of the function to be minimized. While this can be justified when the function has a very complicated microstructure, it results in an unnecessary loss of efficiency when the landscape is smooth but anisotropic. To overcome this deficiency, we propose a random minimization algorithm with adaptive memory: the algorithm decides by itself how much of the information gathered through the process of minimizing the function can be successfully used to guide the search. Extensive experiments (minimization of quadratic forms, computation of the minimum eigenvalue of positive definite quadratic forms of high dimensionality, eigenvalue computation in Hilbert spaces and fitting of data by superposition of Gaussians) show that efficiency is increased and that the algorithm is able to adapt quickly to the current landscape.