The objective of this book is to present new algorithms with faster convergence rates. This is achieved by using dynamical systems. The examples are the golden section algorithm of line search, the ellipsoid algorithms of linear and convex programming, and a standard steepest descent algorithm. Using a Bayesian approach, with a priori distribution for the search object, the authors show that algorithms with improved asymptotic expected performances can be constructed. An important step consists in deriving algorithms with good performance and with a finite and small number of iterations from algorithms with good ergodic performance. A link between algorithms and dynamical systems is exploited to improve rates of convergence.